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Permutation and CombinationQuestion and Answers: Page 16

Question Number 94397 Answers: 1 Comments: 0

Question Number 94352 Answers: 0 Comments: 4

Question Number 93764 Answers: 0 Comments: 3

define Σ_(x=0) ^k ((n!)/(x!(n−x)!)) without Σ symbol

$define$ $\underset{x = 0}{\sum^{k}} \frac{n!}{x! (n - x)!}$ $without Σ symbol$

Question Number 93450 Answers: 2 Comments: 0

what is the value of coefficient of x^9 in expansion (1+x)(1+x^2 ) (1+x^3 )(1+x^4 )×...×(1+x^(100) ) ?

$what is the value of coefficient$ $of x^{9} in expansion (1 + x) (1 + x^{2})$ $(1 + x^{3}) (1 + x^{4}) \times . . . \times (1 + x^{100}) ?$

Question Number 92923 Answers: 1 Comments: 0

Solve 1+(x/(2!))+(x^2 /(4!))+(x^3 /(6!))+∙∙∙ =0

$Solve$ $1 + \frac{x}{2!} + \frac{x^{2}}{4!} + \frac{x^{3}}{6!} + \cdot \cdot \cdot = 0$

Question Number 92319 Answers: 0 Comments: 3

log _9 (x+(7/2)).log _(3/4) (x^2 ) ≥ log _(3/4) (x+(7/2))

$\log_{9} (x + \frac{7}{2}) . \log_{3 / 4} (x^{2}) ⩾$ $\log_{3 / 4} (x + \frac{7}{2})$

Question Number 91230 Answers: 2 Comments: 0

Σ_(j=o) ^m ^a C_j ^b C_(m−j) = ^(a+b) C_m solve this problem

$\underset{j = o}{\sum^{m}} \overset{a}{} C_{j} \overset{b}{} C_{m - j} = \overset{a + b}{} C_{m}$ $s o l v e t h i s p r o b l e m$

Question Number 90531 Answers: 0 Comments: 2

Please help me to find the value of ′n′ C_8 ^(n+3) =C_(20) ^(n+3)

$P l e a s e h e l p m e t o f i n d t h e v a l u e$ $o f^{'} n^{'}$ $C_{8}^{n + 3} = C_{20}^{n + 3}$

Question Number 90503 Answers: 0 Comments: 2

Question Number 88876 Answers: 0 Comments: 2

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...

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

Question Number 87975 Answers: 0 Comments: 7

Question Number 87933 Answers: 0 Comments: 10

how many terms are there in (x^2 +x+1)^(11) ?

$how many terms are there$ $in {(x^{2} + x + 1)}^{11} ?$

Question Number 87790 Answers: 2 Comments: 0

How many handshakes are exchanged betwen 27 boys?

$How many handshakes are exchanged$ $betwen 27 boys ?$

Question Number 87732 Answers: 0 Comments: 1

Solve it in N C_n ^3 −C_n ^2 =5+((n^3 −6n^2 )/6)

$Solve it in N$ $C_{n}^{3} - C_{n}^{2} = 5 + \frac{n^{3} - {6 n}^{2}}{6}$

Question Number 87731 Answers: 0 Comments: 1

solve in N A_n ^4 =A_n ^3

$solve in N$ $A_{n}^{4} = A_{n}^{3}$

Question Number 87175 Answers: 1 Comments: 2

if in the expansion of (1+x)^n the coefficient of x^9 is the aritmetic mean of the coeficients of x^8 and x^(10) . find the possible value of n where n is a positive integer

$if in the expansion of {(1 + x)}^{n} the$ $coefficient of x^{9} is the aritmetic$ $mean of the coeficients of x^{8} and$ $x^{10} . find the possible value$ $of n where n is a positive integer$

Question Number 87074 Answers: 1 Comments: 4

what is coefficient of t^3 in the expanssion {((1−t^6 )/(1−t))}^3

$what is coefficient of t^{3}$ $in the expanssion {\frac{1 - t^{6}}{1 - t}}^{3}$

Question Number 86684 Answers: 2 Comments: 0

If (1+px+qx^2 )^8 = 1+8x+52x^2 +kx^3 +... find p , q and k.

$If {(1 + px + {qx}^{2})}^{8} = 1 + 8 x + {52 x}^{2} + {kx}^{3} + . . .$ $find p, q and k .$

Question Number 85817 Answers: 2 Comments: 0

what is coefficient of x^2 in the expansion [ (1−x)(1+2x)]^6

$what is coefficient of x^{2} in$ $the expansion {[(1 - x) (1 + 2 x)]}^{6}$

Question Number 85583 Answers: 0 Comments: 0

Question Number 85187 Answers: 0 Comments: 0

Show that ∀ n, p ∈ N^(∗ ) C_(n−1) ^( p−1) +C_(n−1) ^( p) =C_n ^( p)

$S h o w t h a t \forall n, p \in N^{*}$ $C_{n - 1}^{p - 1} + C_{n - 1}^{p} = C_{n}^{p}$

Question Number 84998 Answers: 2 Comments: 0

what is coefficient of x^(29) in expression (1+x^5 +x^7 +x^9 )^(29)

$what is coefficient of x^{29}$ $in expression {(1 + x^{5} + x^{7} + x^{9})}^{29}$

Question Number 84993 Answers: 2 Comments: 7

100 apples should be packed in three boxes and each box should contain at least 10 apples. in how many ways can this be done?

$100 a p p l e s s h o u l d b e p a c k e d i n t h r e e$ $b o x e s a n d e a c h b o x s h o u l d c o n t a i n$ $a t l e a s t 10 a p p l e s . i n h o w m a n y w a y s$ $c a n t h i s b e d o n e ?$

Question Number 84261 Answers: 3 Comments: 0

Question Number 84125 Answers: 0 Comments: 0

is it possible to find the no. of positive integral solutions of x+y+2z+3c=7

$i s i t p o s s i b l e t o f i n d$ $t h e n o . o f p o s i t i v e$ $i n t e g r a l s o l u t i o n s$ $o f x + y + 2 z + 3 c = 7$

Question Number 82975 Answers: 0 Comments: 7

To the member in forum. please give an opinion on this matter. George , Lucia and 12 of their friends will sit around a round table. Many of their arrangements sit if George and Lucia always flank 5 of their friends?

$To the member in forum . please$ $give an opinion on this matter .$ $George, Lucia and 12 of their$ $friends will sit around a round table .$ $Many of their arrangements sit$ $if George and Lucia always flank$ $5 of their friends ?$

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