Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 10

Question Number 130689 Answers: 0 Comments: 0

Mr. Rahmat decided to create a password with the form numbers and letterse intermittntly intermittent ( can also be letters and numbers intermittently) but no nmbers and letters are the same. It chooses to use numbers on the set {2, 5, 8, 9} and selects the letters on the set { A, X, Y, W,Z} How many passwords can I create

$$ \\ $$$$\mathrm{Mr}.\:\mathrm{Rahmat}\:\mathrm{decided}\:\mathrm{to}\:\mathrm{create}\:\mathrm{a}\:\mathrm{password}\: \\ $$$$\mathrm{with}\:\mathrm{the}\:\mathrm{form}\:\mathrm{numbers}\:\mathrm{and}\:\mathrm{letterse} \\ $$$$\mathrm{intermittntly}\:\:\mathrm{intermittent}\:\left(\:\mathrm{can}\:\mathrm{also}\:\mathrm{be}\right. \\ $$$$\left.\mathrm{letters}\:\mathrm{and}\:\mathrm{numbers}\:\mathrm{intermittently}\right)\:\mathrm{but}\:\mathrm{no} \\ $$$$\mathrm{nmbers}\:\mathrm{and}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{the}\:\mathrm{same}.\:\mathrm{It}\: \\ $$$$\mathrm{chooses}\:\mathrm{to}\:\mathrm{use}\:\mathrm{numbers}\:\mathrm{on}\:\mathrm{the}\:\mathrm{set}\:\:\left\{\mathrm{2},\:\mathrm{5},\:\mathrm{8},\:\mathrm{9}\right\}\: \\ $$$$\mathrm{and}\:\mathrm{selects}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{on}\:\mathrm{the}\:\mathrm{set}\:\left\{\:\mathrm{A},\:\mathrm{X},\:\mathrm{Y},\:\mathrm{W},\mathrm{Z}\right\}\: \\ $$$$\:\mathrm{How}\:\mathrm{many}\:\mathrm{passwords}\:\mathrm{can}\:\mathrm{I}\:\mathrm{create}\: \\ $$

Question Number 130634 Answers: 1 Comments: 0

Question Number 130602 Answers: 1 Comments: 0

Question Number 130193 Answers: 2 Comments: 0

How many words with at least 2 letters can be formed from UNUSUALNESS?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{words}\:\mathrm{with}\:\mathrm{at}\:\mathrm{least}\:\mathrm{2}\:\mathrm{letters} \\ $$$$\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\boldsymbol{\mathrm{UNUSUALNESS}}? \\ $$

Question Number 130034 Answers: 1 Comments: 0

How many integers between 999 and 4000 (both are included) can be formed using digits 0,1,2,3,4 if repetition of digits is allowed?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{integers}\:\mathrm{between}\:\mathrm{999}\:\mathrm{and}\:\mathrm{4000} \\ $$$$\left(\mathrm{both}\:\mathrm{are}\:\mathrm{included}\right)\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{using} \\ $$$$\mathrm{digits}\:\mathrm{0},\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4}\:\mathrm{if}\:\mathrm{repetition}\:\mathrm{of}\:\mathrm{digits}\:\mathrm{is} \\ $$$$\mathrm{allowed}?\: \\ $$

Question Number 130019 Answers: 1 Comments: 0

How many 4 letters word can be formed from COMMUNICATION

$$\mathrm{How}\:\mathrm{many}\:\mathrm{4}\:\mathrm{letters}\:\mathrm{word}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\:\:\:\mathrm{COMMUNICATION} \\ $$

Question Number 125548 Answers: 1 Comments: 2

How many four−digit numbers between 2000 and 4000 can be formed from the numbers 0, 1, 2, 3, 4 and 5 if repitition is allowed?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{four}−\mathrm{digit}\:\mathrm{numbers}\: \\ $$$$\mathrm{between}\:\mathrm{2000}\:\mathrm{and}\:\mathrm{4000}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{0},\:\mathrm{1},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4}\:\mathrm{and}\:\mathrm{5}\: \\ $$$$\mathrm{if}\:\mathrm{repitition}\:\mathrm{is}\:\mathrm{allowed}? \\ $$

Question Number 125460 Answers: 1 Comments: 0

In a room containing N people N>3, at least one person has not shaken hands with everyone else in the room. What is the maximum number of people in the room that could have shaken hands with everyone else?

$$\:{In}\:{a}\:{room}\:{containing}\:{N}\:{people} \\ $$$${N}>\mathrm{3},\:{at}\:{least}\:{one}\:{person}\:{has}\:{not} \\ $$$${shaken}\:{hands}\:{with}\:{everyone} \\ $$$${else}\:{in}\:{the}\:{room}.\:{What}\:{is}\:{the}\: \\ $$$${maximum}\:{number}\:{of}\:{people}\: \\ $$$${in}\:{the}\:{room}\:{that}\:{could}\:{have}\: \\ $$$${shaken}\:{hands}\:{with}\:{everyone}\: \\ $$$${else}?\: \\ $$

Question Number 125208 Answers: 1 Comments: 0

There are 12 students in a party. Five of them are girls. In how many ways can these 12 students be arranged in a row if (i) there are no restrictions? (ii) the 5 girls must be together (forming a block)? (iii) no 2 girls are adjacent (iv) between two particular boys A and B , there no boys but exactly 3 girls?

$${There}\:{are}\:\mathrm{12}\:{students}\:{in}\:{a}\:{party}.\:{Five}\:{of} \\ $$$${them}\:{are}\:{girls}.\:{In}\:{how}\:{many}\:{ways}\:{can}\: \\ $$$${these}\:\mathrm{12}\:{students}\:{be}\:{arranged}\:{in}\:{a}\:{row}\:{if}\: \\ $$$$\left({i}\right)\:{there}\:{are}\:{no}\:{restrictions}? \\ $$$$\left({ii}\right)\:{the}\:\mathrm{5}\:{girls}\:{must}\:{be}\:{together}\:\left({forming}\:{a}\:{block}\right)? \\ $$$$\left({iii}\right)\:{no}\:\mathrm{2}\:{girls}\:{are}\:{adjacent}\: \\ $$$$\left({iv}\right)\:{between}\:{two}\:{particular}\:{boys}\:{A}\:{and}\:{B}\: \\ $$$$\:,\:{there}\:{no}\:{boys}\:{but}\:{exactly}\:\mathrm{3}\:{girls}? \\ $$

Question Number 125207 Answers: 2 Comments: 0

Find the number of ways to choose a pair {a,b} of distinct numbers from the set {1,2,3,...,50} such that (i) ∣a−b∣ = 5 (ii) ∣a−b∣ ≤ 5

$${Find}\:{the}\:{number}\:{of}\:{ways}\:{to}\:{choose}\:{a}\:{pair} \\ $$$$\left\{{a},{b}\right\}\:{of}\:{distinct}\:{numbers}\:{from}\:{the}\:{set}\: \\ $$$$\left\{\mathrm{1},\mathrm{2},\mathrm{3},...,\mathrm{50}\right\}\:{such}\:{that}\: \\ $$$$\left({i}\right)\:\mid{a}−{b}\mid\:=\:\mathrm{5} \\ $$$$\left({ii}\right)\:\mid{a}−{b}\mid\:\leqslant\:\mathrm{5}\: \\ $$

Question Number 125191 Answers: 0 Comments: 4

In how many ways can 3 men and 5 women be seated in a row if 3 specific women cannot sit next to each other? My solution: arrangements when the 3 women cannot sit next to eachother = 5! ×^6 P_3 = 14,400 Solution in book: arrangements with no restrictions = 8! arrangements with the 3 women seated next to eachother = 3! × 6! arrangements when the 3 women cannot sit next to eachother = 8! − (3! × 6!) = 36,000 I′m confused. Can I please get some explanation why my solution is wrong?

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{3}\:\mathrm{men}\:\mathrm{and}\:\mathrm{5} \\ $$$$\mathrm{women}\:\mathrm{be}\:\mathrm{seated}\:\mathrm{in}\:\mathrm{a}\:\mathrm{row}\:\mathrm{if}\:\mathrm{3}\:\mathrm{specific} \\ $$$$\mathrm{women}\:{cannot}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}? \\ $$$$ \\ $$$$\mathrm{My}\:\mathrm{solution}: \\ $$$$\mathrm{arrangements}\:\mathrm{when}\:\mathrm{the}\:\mathrm{3}\:\mathrm{women} \\ $$$${cannot}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{eachother}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{5}!\:×\:^{\mathrm{6}} {P}_{\mathrm{3}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{14},\mathrm{400} \\ $$$$ \\ $$$$\mathrm{Solution}\:\mathrm{in}\:\mathrm{book}: \\ $$$$\mathrm{arrangements}\:\mathrm{with}\:\mathrm{no}\:\mathrm{restrictions}\:=\:\mathrm{8}! \\ $$$$ \\ $$$$\mathrm{arrangements}\:\mathrm{with}\:\mathrm{the}\:\mathrm{3}\:\mathrm{women} \\ $$$$\mathrm{seated}\:\mathrm{next}\:\mathrm{to}\:\mathrm{eachother}\:\:=\:\:\mathrm{3}!\:×\:\mathrm{6}! \\ $$$$ \\ $$$$\mathrm{arrangements}\:\mathrm{when}\:\mathrm{the}\:\mathrm{3}\:\mathrm{women} \\ $$$${cannot}\:\mathrm{sit}\:\mathrm{next}\:\mathrm{to}\:\mathrm{eachother}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{8}!\:−\:\left(\mathrm{3}!\:×\:\mathrm{6}!\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\:\mathrm{36},\mathrm{000} \\ $$$$ \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{confused}.\:\mathrm{Can}\:\mathrm{I}\:\mathrm{please}\:\mathrm{get}\:\mathrm{some} \\ $$$$\mathrm{explanation}\:\mathrm{why}\:\mathrm{my}\:\mathrm{solution}\:\mathrm{is}\:\mathrm{wrong}? \\ $$

Question Number 124916 Answers: 2 Comments: 0

The number of ways arrangements of the word ′MASKARA′ with exactly 2 A′s are adjacent??

$${The}\:{number}\:{of}\:{ways}\:{arrangements}\: \\ $$$${of}\:{the}\:{word}\:'{MASKARA}'\:{with}\:{exactly} \\ $$$$\mathrm{2}\:{A}'{s}\:\:{are}\:{adjacent}??\: \\ $$

Question Number 124878 Answers: 3 Comments: 0

20 students should stand in 5 different rows. each row should have at least 2 students. in how many ways can you arrange them?

$$\mathrm{20}\:{students}\:{should}\:{stand}\:{in}\:\mathrm{5} \\ $$$${different}\:{rows}.\:{each}\:{row}\:{should}\:{have} \\ $$$${at}\:{least}\:\mathrm{2}\:{students}.\:{in}\:{how}\:{many}\:{ways} \\ $$$${can}\:{you}\:{arrange}\:{them}? \\ $$

Question Number 124829 Answers: 2 Comments: 0

How many ways are there to arrange the letters of the word ′ALAMATAR′ if no two A′s are adjacent?

$$\:{How}\:{many}\:{ways}\:{are}\:{there}\:{to}\:{arrange} \\ $$$${the}\:{letters}\:{of}\:{the}\:{word}\:'{ALAMATAR}'\:{if} \\ $$$${no}\:{two}\:{A}'{s}\:{are}\:{adjacent}?\: \\ $$

Question Number 124826 Answers: 2 Comments: 0

How many ways are there to arrange the letters of the word ′ VISITING′ if no two I′s are adjacent ?

$$\:{How}\:{many}\:{ways}\:{are}\:{there}\:{to}\:{arrange}\: \\ $$$${the}\:{letters}\:{of}\:{the}\:{word}\:'\:{VISITING}' \\ $$$${if}\:{no}\:{two}\:{I}'{s}\:{are}\:{adjacent}\:? \\ $$

Question Number 124806 Answers: 2 Comments: 0

Question Number 124712 Answers: 2 Comments: 0

In how many ways can 5 boys and 3 girls be seated around a table if (i) boy B_3 and G_2 are not adjacent (ii) no girls are adjacent

$${In}\:{how}\:{many}\:{ways}\:\:{can}\:\mathrm{5}\:{boys}\:{and}\:\mathrm{3}\:{girls} \\ $$$${be}\:{seated}\:{around}\:{a}\:{table}\:{if}\: \\ $$$$\left({i}\right)\:{boy}\:{B}_{\mathrm{3}} \:{and}\:{G}_{\mathrm{2}} \:{are}\:{not}\:{adjacent} \\ $$$$\left({ii}\right)\:{no}\:{girls}\:{are}\:{adjacent}\: \\ $$

Question Number 124709 Answers: 2 Comments: 0

Between 20000 and 70000 find the number of even integers in which no digits is repeated

$${Between}\:\mathrm{20000}\:{and}\:\mathrm{70000}\: \\ $$$${find}\:{the}\:{number}\:{of}\:{even}\:{integers} \\ $$$${in}\:{which}\:{no}\:{digits}\:{is}\:{repeated} \\ $$

Question Number 124678 Answers: 0 Comments: 0

Question Number 124400 Answers: 2 Comments: 0

How many six-digit numbers contain exactly three different digits?

$${How}\:{many}\:{six}-{digit}\:{numbers}\:{contain} \\ $$$${exactly}\:{three}\:{different}\:{digits}? \\ $$

Question Number 124372 Answers: 1 Comments: 0

How many six-digit numbers contain exactly six different digits?

$${How}\:{many}\:{six}-{digit}\:{numbers}\:{contain} \\ $$$${exactly}\:{six}\:{different}\:{digits}? \\ $$

Question Number 124237 Answers: 1 Comments: 1

How many 6 digit odd numbers have different digits?

$${How}\:{many}\:\mathrm{6}\:{digit}\:{odd}\:{numbers}\:{have} \\ $$$${different}\:{digits}? \\ $$

Question Number 124173 Answers: 1 Comments: 0

Question Number 123878 Answers: 1 Comments: 0

Nine chairs in a row are to be occupied by six students and Prof George , Prof Pieter, and Prof John. These three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professor George , Pieter and John choose their chairs ?

$${Nine}\:{chairs}\:{in}\:{a}\:{row}\:{are}\:{to}\:{be}\:{occupied}\:{by} \\ $$$${six}\:{students}\:{and}\:{Prof}\:{George}\:,\:{Prof}\:{Pieter}, \\ $$$${and}\:{Prof}\:{John}.\:{These}\:{three}\:{professors}\:{arrive} \\ $$$${before}\:{the}\:{six}\:{students}\:{and}\:{decide}\:{to}\:{choose} \\ $$$${their}\:{chairs}\:{so}\:{that}\:{each}\:{professor}\:{will}\:{be}\:{between} \\ $$$${two}\:{students}.\:{In}\:{how}\:{many}\:{ways}\:{can}\:{Professor}\:{George} \\ $$$$,\:{Pieter}\:{and}\:{John}\:{choose}\:{their}\:{chairs}\:?\: \\ $$

Question Number 123695 Answers: 1 Comments: 0

There are how many ways to answer 5 out of 7 multiple choice question with 5 choices?

$$\boldsymbol{\mathrm{There}}\:\boldsymbol{\mathrm{are}}\:\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{many}}\:\boldsymbol{\mathrm{ways}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{answer}} \\ $$$$\mathrm{5}\:\boldsymbol{\mathrm{out}}\:\boldsymbol{\mathrm{of}}\:\mathrm{7}\:\boldsymbol{\mathrm{multiple}}\:\boldsymbol{\mathrm{choice}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{with}} \\ $$$$\mathrm{5}\:\boldsymbol{\mathrm{choices}}? \\ $$

Question Number 123577 Answers: 1 Comments: 0

Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14

Contact: info@tinkutara.com