Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 8

Question Number 142618 Answers: 0 Comments: 2

In how many ways can committee of 5 be formed from a group of 11 people consisting of 4 teachers and 7 students if there is no restriction in the selection ? _______________________

$$\:\:\:{In}\:{how}\:{many}\:{ways}\:{can}\:{committee} \\ $$$${of}\:\mathrm{5}\:{be}\:{formed}\:{from}\:{a}\:{group}\: \\ $$$${of}\:\mathrm{11}\:{people}\:{consisting}\:{of}\:\mathrm{4}\:{teachers} \\ $$$${and}\:\mathrm{7}\:{students}\:{if}\:{there}\:{is}\:{no}\: \\ $$$${restriction}\:{in}\:{the}\:{selection}\:? \\ $$$$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \\ $$

Question Number 142305 Answers: 1 Comments: 0

Question Number 141777 Answers: 0 Comments: 1

A pack of 52 cards distributed equally to 4 people so as 4 cards each from same suit( of any 3 suit=4×3=12) and last card from 4th remaining suit . Number of such distributions is?

$${A}\:{pack}\:{of}\:\mathrm{52}\:{cards}\:{distributed}\:{equally}\:{to} \\ $$$$\mathrm{4}\:{people}\:{so}\:{as}\:\mathrm{4}\:{cards}\:{each}\:{from}\: \\ $$$${same}\:{suit}\left(\:{of}\:{any}\:\mathrm{3}\:{suit}=\mathrm{4}×\mathrm{3}=\mathrm{12}\right) \\ $$$${and}\:{last}\:{card}\:{from}\:\mathrm{4}{th}\:{remaining} \\ $$$${suit}\:.\:{Number}\:{of}\:{such} \\ $$$${distributions}\:{is}? \\ $$$$ \\ $$$$ \\ $$

Question Number 141435 Answers: 1 Comments: 0

Find all the arraangment of all the letters of the word SYLLABUSES such that each word contains the word BUS.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{arraangment}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{SYLLABUSES}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{word}\:\mathrm{contains}\:\mathrm{the}\:\mathrm{word}\:\mathrm{BUS}. \\ $$

Question Number 139352 Answers: 0 Comments: 1

Question Number 139332 Answers: 1 Comments: 0

Find the coefficient of x^(50) in the expression (1+x)^(1000) +2x(1+x)^(999) + 3x^2 (1+x)^(998) +...+1001x^(1000)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{50}} \:\mathrm{in} \\ $$$$\mathrm{the}\:\mathrm{expression}\:\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{1000}} \:+\mathrm{2x}\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{999}} + \\ $$$$\mathrm{3x}^{\mathrm{2}} \left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{998}} +...+\mathrm{1001x}^{\mathrm{1000}} \\ $$

Question Number 139286 Answers: 0 Comments: 1

(1/((1−x)^n ))=( ((n),(0) ))+( ((n),(1) ))x+( ((n),(2) ))x^2 +( ((n),(3) ))x^3 +...

$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}} }=\left(\begin{pmatrix}{{n}}\\{\mathrm{0}}\end{pmatrix}\right)+\left(\begin{pmatrix}{{n}}\\{\mathrm{1}}\end{pmatrix}\right){x}+\left(\begin{pmatrix}{{n}}\\{\mathrm{2}}\end{pmatrix}\right){x}^{\mathrm{2}} +\left(\begin{pmatrix}{{n}}\\{\mathrm{3}}\end{pmatrix}\right){x}^{\mathrm{3}} +... \\ $$

Question Number 138748 Answers: 1 Comments: 0

A committee of 3 members is to be formed from 8 members. Find the number of committees that can be formed if two particular club members cannot both be in a committee

$$\mathrm{A}\:\mathrm{committee}\:\mathrm{of}\:\mathrm{3}\:\mathrm{members}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{from}\:\mathrm{8}\:\mathrm{members}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{committees}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{formed}\:\mathrm{if}\:\mathrm{two}\:\mathrm{particular} \\ $$$$\mathrm{club}\:\mathrm{members}\:\mathrm{cannot}\:\mathrm{both}\:\mathrm{be}\:\mathrm{in}\:\mathrm{a}\:\mathrm{committee} \\ $$

Question Number 137943 Answers: 1 Comments: 0

Determine the term independent of x in the expansion (((x+1)/(x^(2/3) −x^(1/3) +1)) −((x−1)/(x−x^(1/2) )) )^(10) .

$${Determine}\:{the}\:{term}\:{independent} \\ $$$${of}\:{x}\:{in}\:{the}\:{expansion}\: \\ $$$$\:\:\:\:\left(\frac{{x}+\mathrm{1}}{{x}^{\mathrm{2}/\mathrm{3}} −{x}^{\mathrm{1}/\mathrm{3}} +\mathrm{1}}\:−\frac{{x}−\mathrm{1}}{{x}−{x}^{\mathrm{1}/\mathrm{2}} }\:\right)^{\mathrm{10}} \:. \\ $$

Question Number 137745 Answers: 1 Comments: 0

Each of the digits 2, 4, 6, and 8 can be used once and once only in writing a four-digit number. What is the sum of all such numbers that are divisible by 11?

$$ \\ $$Each of the digits 2, 4, 6, and 8 can be used once and once only in writing a four-digit number. What is the sum of all such numbers that are divisible by 11?

Question Number 137035 Answers: 1 Comments: 1

Given a 10−digit number X = 1345789026 How many 10−digit number that can be made using every digit from X, with condition: If a number n is located in k^(th) position of X, then the new created number must not contain number n in k^(th) position Example: • Number 1 is located in 1^(st) position of X, hence 1234567890 is not valid, but 2134567890 is valid • Number 5 and 0 are located in 4^(th) and 8^(th) position of X, hence 9435162087 is not valid, but 9431506287 is valid. • 1345026789 is not valid • and so on...

$$\mathrm{Given}\:\mathrm{a}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:{X}\:=\:\mathrm{1345789026} \\ $$$$\mathrm{How}\:\mathrm{many}\:\mathrm{10}−\mathrm{digit}\:\mathrm{number}\:\mathrm{that}\:\mathrm{can}\:\mathrm{be}\:\mathrm{made} \\ $$$$\mathrm{using}\:\mathrm{every}\:\mathrm{digit}\:\mathrm{from}\:{X},\:\mathrm{with}\:\mathrm{condition}: \\ $$$$\mathrm{If}\:\mathrm{a}\:\mathrm{number}\:{n}\:\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{then} \\ $$$$\mathrm{the}\:\mathrm{new}\:\mathrm{created}\:\mathrm{number}\:\mathrm{must}\:\mathrm{not}\:\mathrm{contain} \\ $$$$\mathrm{number}\:{n}\:\mathrm{in}\:{k}^{{th}} \:\mathrm{position} \\ $$$$ \\ $$$$\mathrm{Example}: \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{1}\:\mathrm{is}\:\mathrm{located}\:\mathrm{in}\:\mathrm{1}^{{st}} \:\mathrm{position}\:\mathrm{of}\:{X},\:\mathrm{hence} \\ $$$$\mathrm{1234567890}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but}\:\mathrm{2134567890} \\ $$$$\mathrm{is}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{Number}\:\mathrm{5}\:\mathrm{and}\:\mathrm{0}\:\mathrm{are}\:\mathrm{located}\:\mathrm{in}\:\mathrm{4}^{{th}} \:\mathrm{and}\:\mathrm{8}^{{th}} \:\mathrm{position} \\ $$$$\mathrm{of}\:{X},\:\mathrm{hence}\:\mathrm{9435162087}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid},\:\mathrm{but} \\ $$$$\mathrm{9431506287}\:\mathrm{is}\:\mathrm{valid}. \\ $$$$\bullet\:\mathrm{1345026789}\:\mathrm{is}\:\mathrm{not}\:\mathrm{valid} \\ $$$$\bullet\:\mathrm{and}\:\mathrm{so}\:\mathrm{on}... \\ $$

Question Number 136872 Answers: 0 Comments: 4

Question Number 136448 Answers: 1 Comments: 0

Mr.A wants to deliver 7 letters to his 7 friends so that each gets 1 letter. All of the letters are written of the addresses of his 7 friends. Find the probbility that, 3 of his friends receive the correct letters and the remaining 4 receive the wrong ones.

$$\mathrm{Mr}.\mathrm{A}\:\mathrm{wants}\:\mathrm{to}\:\mathrm{deliver}\:\mathrm{7}\:\mathrm{letters}\:\mathrm{to}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}\:\mathrm{so}\:\mathrm{that}\:\mathrm{each}\:\mathrm{gets}\:\mathrm{1}\:\mathrm{letter}. \\ $$$$\mathrm{All}\:\mathrm{of}\:\mathrm{the}\:\mathrm{letters}\:\mathrm{are}\:\mathrm{written}\:\mathrm{of}\:\mathrm{the}\:\mathrm{addresses}\:\mathrm{of}\:\mathrm{his}\:\mathrm{7}\:\mathrm{friends}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{probbility}\:\mathrm{that}, \\ $$$$\mathrm{3}\:\mathrm{of}\:\mathrm{his}\:\mathrm{friends}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{correct}\:\mathrm{letters}\:\mathrm{and}\:\mathrm{the}\:\mathrm{remaining}\:\mathrm{4}\:\mathrm{receive}\:\mathrm{the}\:\mathrm{wrong}\:\mathrm{ones}. \\ $$

Question Number 136417 Answers: 2 Comments: 0

Question Number 135797 Answers: 1 Comments: 0

How do you solve f(3) when f(-1) = -1 and f(0) =1 and f(x) =f(x-1)-2f(x-2)?

$$ \\ $$How do you solve f(3) when f(-1) = -1 and f(0) =1 and f(x) =f(x-1)-2f(x-2)?

Question Number 135599 Answers: 1 Comments: 0

Question Number 135490 Answers: 3 Comments: 0

Combination A committee of 8 people is to be formed from 7 women and 5 men. In how many ways can the members be chosen so as to include at least 3 men?

$${Combination} \\ $$A committee of 8 people is to be formed from 7 women and 5 men. In how many ways can the members be chosen so as to include at least 3 men?

Question Number 135303 Answers: 2 Comments: 0

in how many ways can 10 people be seated in a round table if 3 persons want to seat consecutively?

$$ \\ $$in how many ways can 10 people be seated in a round table if 3 persons want to seat consecutively?

Question Number 135239 Answers: 0 Comments: 0

Question Number 135218 Answers: 2 Comments: 0

Permutation How many ways can 10 men and 7 women sit at a round table so that no 2 women are next to each other? 😎😎😎😎

$$\mathrm{Permutation} \\ $$How many ways can 10 men and 7 women sit at a round table so that no 2 women are next to each other? 😎😎😎😎

Question Number 135024 Answers: 0 Comments: 7

Question Number 134905 Answers: 2 Comments: 1

Combinatorics What is the number of ways of distributing 9 different objects among 5 persons such that each gets at least 1?

$$\mathrm{Combinatorics} \\ $$What is the number of ways of distributing 9 different objects among 5 persons such that each gets at least 1?

Question Number 134798 Answers: 3 Comments: 0

Binomial theorem Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5 is 1440, what is the value of the constant a?

$$\mathrm{Binomial}\:\mathrm{theorem} \\ $$Given that the coefficient of x^2 in the expansion of (1+ax) (3-2 x) ^5 is 1440, what is the value of the constant a?

Question Number 134644 Answers: 1 Comments: 1

Question Number 134482 Answers: 0 Comments: 5

How many ways can this be done if you distribute 25 identical pieces of candy among five children?

$$ \\ $$How many ways can this be done if you distribute 25 identical pieces of candy among five children?

Question Number 134389 Answers: 1 Comments: 0

Eight dice are tossed. If the dice are identical in appearance , how many different−looking (distinguishable) occurrences are there?

$$\mathrm{Eight}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{tossed}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{dice}\:\mathrm{are}\:\mathrm{identical}\:\mathrm{in} \\ $$$$\mathrm{appearance}\:,\:\mathrm{how}\:\mathrm{many}\:\mathrm{different}−\mathrm{looking}\: \\ $$$$\left(\mathrm{distinguishable}\right)\:\mathrm{occurrences}\:\mathrm{are}\:\mathrm{there}? \\ $$

Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12

Contact: info@tinkutara.com