Question and Answers Forum

Permutation and CombinationQuestion and Answers: Page 6

Question Number 159715 Answers: 0 Comments: 1

Question Number 159259 Answers: 1 Comments: 0

montre que Σ_(k=0) ^n C_(2n) ^(2k) =2^(2n−1)

$$\boldsymbol{{montre}}\:\boldsymbol{{que}}\: \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{C}}_{\mathrm{2}\boldsymbol{{n}}} ^{\mathrm{2}\boldsymbol{{k}}} =\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} \\ $$

Question Number 158955 Answers: 1 Comments: 0

Question Number 158529 Answers: 1 Comments: 0

In how many ways can 30 students be distributed to 10 schools, if 1. each school should get at least one student. 2. no restriction

$${In}\:{how}\:{many}\:{ways}\:{can}\:\mathrm{30}\:{students} \\ $$$${be}\:{distributed}\:{to}\:\mathrm{10}\:{schools},\:{if} \\ $$$$\mathrm{1}.\:{each}\:{school}\:{should}\:{get}\:{at}\:{least}\:{one} \\ $$$$\:\:\:\:\:{student}. \\ $$$$\mathrm{2}.\:{no}\:{restriction} \\ $$

Question Number 157980 Answers: 2 Comments: 0

Calculate this problem below a). ((7!)/((5−1)!)) =...... b). ((5!×3!)/(4!)) =...... c). 6! 4! =... d). ((7!)/(3!))×((2!)/(5!)) =......

$$\mathrm{Calculate}\:\mathrm{this}\:\mathrm{problem}\:\mathrm{below} \\ $$$$\left.\:\:\:\:\:\:\:\:\mathrm{a}\right).\:\:\frac{\mathrm{7}!}{\left(\mathrm{5}−\mathrm{1}\right)!}\:=...... \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\mathrm{b}\right).\:\:\frac{\mathrm{5}!×\mathrm{3}!}{\mathrm{4}!}\:=...... \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}\right).\:\:\mathrm{6}!\:\mathrm{4}!\:=...\:\:\:\:\:\:\:\: \\ $$$$\left.\:\:\:\:\:\:\:\:\:\:\:\mathrm{d}\right).\:\:\frac{\mathrm{7}!}{\mathrm{3}!}×\frac{\mathrm{2}!}{\mathrm{5}!}\:=...... \\ $$

Question Number 157126 Answers: 0 Comments: 9

how many ways can you exchange 1 dollar using (1,5,10,25,50) cents example 1 dollar(100 cents)=2×50cents =1×50+2×25=4×25 =1×50+1×25+1×10+1×5+10×1 and so on how many all the ways ?

$${how}\:{many}\:{ways}\:{can}\:{you} \\ $$$${exchange}\:\mathrm{1}\:{dollar}\:{using} \\ $$$$\left(\mathrm{1},\mathrm{5},\mathrm{10},\mathrm{25},\mathrm{50}\right)\:{cents} \\ $$$${example} \\ $$$$\mathrm{1}\:{dollar}\left(\mathrm{100}\:{cents}\right)=\mathrm{2}×\mathrm{50}{cents} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{2}×\mathrm{25}=\mathrm{4}×\mathrm{25} \\ $$$$=\mathrm{1}×\mathrm{50}+\mathrm{1}×\mathrm{25}+\mathrm{1}×\mathrm{10}+\mathrm{1}×\mathrm{5}+\mathrm{10}×\mathrm{1} \\ $$$${and}\:{so}\:{on} \\ $$$${how}\:{many}\:{all}\:{the}\:{ways}\:? \\ $$

Question Number 156979 Answers: 2 Comments: 2

Question Number 155842 Answers: 1 Comments: 1

Prof that: Σ_(n=1) ^(10) n.n!=11!−1

$$\mathrm{Prof}\:\mathrm{that}: \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{n}.\mathrm{n}!=\mathrm{11}!−\mathrm{1} \\ $$

Question Number 155816 Answers: 1 Comments: 0

How many of the number formed by using all the digits 1,2,3,4,5,6 only once divisible by 25.

$$\:\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\mathrm{formed} \\ $$$$\:\mathrm{by}\:\mathrm{using}\:\mathrm{all}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6} \\ $$$$\:\mathrm{only}\:\mathrm{once}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{25}. \\ $$

Question Number 155356 Answers: 0 Comments: 0

Find the coefficient of term “ a^m b^(2m) ” in (1+a)^m (1+b)^(n+m) (1+a+b)^m .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{term}\:``\:\mathrm{a}^{\mathrm{m}} \mathrm{b}^{\mathrm{2m}} \:''\:\mathrm{in}\:\left(\mathrm{1}+\mathrm{a}\right)^{\mathrm{m}} \left(\mathrm{1}+\mathrm{b}\right)^{\mathrm{n}+\mathrm{m}} \left(\mathrm{1}+\mathrm{a}+\mathrm{b}\right)^{\mathrm{m}} . \\ $$

Question Number 155109 Answers: 1 Comments: 0

how many terms contain “ ab^2 c^3 ” in (a+2b+3c+4d^2 +5e^3 )^(10) ?

$$\mathrm{how}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{contain}\:``\:\mathrm{ab}^{\mathrm{2}} \mathrm{c}^{\mathrm{3}} \:''\:\mathrm{in}\:\left(\mathrm{a}+\mathrm{2b}+\mathrm{3c}+\mathrm{4d}^{\mathrm{2}} +\mathrm{5e}^{\mathrm{3}} \right)^{\mathrm{10}} \:? \\ $$

Question Number 155075 Answers: 1 Comments: 4

Question Number 155257 Answers: 1 Comments: 5

Question Number 154287 Answers: 0 Comments: 0

Question Number 154268 Answers: 0 Comments: 3

Question Number 153714 Answers: 2 Comments: 0

How many three−digit numbers can be formed using the digits 2,3,5,7,8 if the number is odd and no digit is repeted?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{three}−\mathrm{digit}\:\mathrm{numbers}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{using}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{2},\mathrm{3},\mathrm{5},\mathrm{7},\mathrm{8}\:\mathrm{if}\: \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{odd}\:\mathrm{and}\:\mathrm{no}\:\mathrm{digit}\:\mathrm{is}\:\mathrm{repeted}? \\ $$

Question Number 153220 Answers: 1 Comments: 0

in how many ways can the number n be written as a sum of three positive integers if representations differing in the order of the terms are considered to be different?

$$\: \\ $$$$\:\mathrm{in}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{the}\:\mathrm{number}\:\: \\ $$$$\:{n}\:\mathrm{be}\:\mathrm{written}\:\mathrm{as}\:\mathrm{a}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{positive}\:\: \\ $$$$\:\mathrm{integers}\:\mathrm{if}\:\mathrm{representations}\:\mathrm{differing}\:\: \\ $$$$\:\mathrm{in}\:\mathrm{the}\:\mathrm{order}\:\mathrm{of}\:\mathrm{the}\:\mathrm{terms}\:\mathrm{are}\:\mathrm{considered}\:\: \\ $$$$\:\mathrm{to}\:\mathrm{be}\:\mathrm{different}?\:\: \\ $$$$\: \\ $$

Question Number 153216 Answers: 0 Comments: 1

$$ \\ $$

Question Number 153181 Answers: 0 Comments: 2