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Permutation and CombinationQuestion and Answers: Page 6

Question Number 166770 Answers: 4 Comments: 6

In how many ways can you go up a staircase with 20 steps if you take one, two or three steps at a time?

$I n h o w m a n y w a y s c a n y o u g o u p a$ $s t a i r c a s e w i t h 20 s t e p s i f y o u t a k e$ $o n e, t w o o r t h r e e s t e p s a t a t i m e ?$

Question Number 166569 Answers: 0 Comments: 0

Question Number 165385 Answers: 1 Comments: 1

Number of ways..n differrnt things be distributed in r identical boxes so as 1)empty box is allowed 2)empty box not allowed Number of ways...n identical things be distributed to r identical boxes so as 1)empty box allowed 2)empty box not allowed

$N u m b e r o f w a y s . . n$ $d i f f e r r n t t h i n g s b e d i s t r i b u t e d$ $i n r i d e n t i c a l b o x e s s o a s$ $1) e m p t y b o x i s a l l o w e d$ $2) e m p t y b o x n o t a l l o w e d$ $N u m b e r o f w a y s . . . n i d e n t i c a l$ $t h i n g s b e d i s t r i b u t e d t o r$ $i d e n t i c a l b o x e s s o a s$ $1) e m p t y b o x a l l o w e d$ $2) e m p t y b o x n o t a l l o w e d$

Question Number 165376 Answers: 1 Comments: 0

Verify wether f is invertible f (x) = (1+2x)^3

$Verify wether f is invertible$ $f (x) = {(1 + 2 x)}^{3}$

Question Number 165361 Answers: 1 Comments: 2

Obtain a general formula for the sequence (2/3),(4/5),(8/9),((16)/(17)),((32)/(33)),... assuming the sequence continues in that pattern.

$Obtain a general formula for$ $the sequence$ $\frac{2}{3}, \frac{4}{5}, \frac{8}{9}, \frac{16}{17}, \frac{32}{33}, . . .$ $assuming the sequence continues in that$ $pattern .$

Question Number 164996 Answers: 1 Comments: 0

Question Number 164588 Answers: 0 Comments: 0

soit K un corps; pour toute permutation σ de S_n , on note P(σ) sa matrice dans la base canonique de K^n . montrer que deux permutations σ_1 et σ_2 sont conjugues dans S_n si et seulement si P(σ_1 ) et P(σ_2 ) sont semblables.

$s o i t K u n c o r p s; p o u r t o u t e p e r m u t a t i o n$ $σ d e S_{n}, o n n o t e P (σ) s a m a t r i c e d a n s l a b a s e$ $c a n o n i q u e d e K^{n} .$ $m o n t r e r q u e d e u x p e r m u t a t i o n s σ_{1} e t σ_{2} s o n t$ $c o n j u g u e s d a n s S_{n} s i e t s e u l e m e n t s i$ $P (σ_{1}) e t P (σ_{2}) s o n t s e m b l a b l e s .$

Question Number 164544 Answers: 2 Comments: 0

prove that Σ_(k=1) ^n ((n),(k) )^2 =(((2n)!)/((n!)^2 ))−1

$p r o v e t h a t \underset{k = 1}{\sum^{n}} {(\begin{matrix} n \\ k \end{matrix})}^{2} = \frac{(2 n)!}{{(n!)}^{2}} - 1$

Question Number 163443 Answers: 0 Comments: 7

p ≤ n find (A_n ^p /A_(n−1) ^p ).

$p ⩽ n$ $find \frac{A_{n}^{p}}{A_{n - 1}^{p}} .$

Question Number 163313 Answers: 1 Comments: 0

Find the non negative integer solutions of 2x+3y+5z=60

$F i n d t h e n o n n e g a t i v e i n t e g e r$ $s o l u t i o n s o f 2 x + 3 y + 5 z = 60$

Question Number 163283 Answers: 1 Comments: 1

hi ! We store 5 objects in three discernible drawers. Suppose that the different ways of carrying out these arrangements are equally probable, calculate the probability that one of the 3 drawers contains at least 3 objects.

$hi!$ We store 5 objects in three discernible drawers. Suppose that the different ways of carrying out these arrangements are equally probable, calculate the probability that one of the 3 drawers contains at least 3 objects.

Question Number 163263 Answers: 1 Comments: 0

Question Number 160980 Answers: 2 Comments: 0

How many ways can 50 people be divided into 3 groups, so that each group contains members equal to a prime number?

$How many ways can 50 people$ $be divided into 3 groups, so$ $that each group contains members$ $equal to a prime number ?$

Question Number 160829 Answers: 0 Comments: 1

Question Number 160665 Answers: 0 Comments: 2

In how many ways can you divide 20 students into 5 groups with 4 students in each group such that any two students don′t meet each other in more than one group.

$I n h o w m a n y w a y s c a n y o u d i v i d e 20$ $s t u d e n t s i n t o 5 g r o u p s w i t h 4 s t u d e n t s$ $i n e a c h g r o u p s u c h t h a t a n y t w o$ $s t u d e n t s {d o n}^{'} t m e e t e a c h o t h e r i n$ $m o r e t h a n o n e g r o u p .$

Question Number 160389 Answers: 0 Comments: 2

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)

$m o n t r e q u e$ $\underset{k = 0}{\sum^{n}} C_{2 n}^{2 k} = 2^{2 n - 1}$

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

$I n h o w m a n y w a y s c a n 30 s t u d e n t s$ $b e d i s t r i b u t e d t o 10 s c h o o l s, i f$ $1 . e a c h s c h o o l s h o u l d g e t a t l e a s t o n e$ $s t u d e n t .$ $2 . n o r e s t r i c t i o n$

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!)) =......

$Calculate this problem below$ $a) . \frac{7!}{(5 - 1)!} = . . . . . .$ $b) . \frac{5! \times 3!}{4!} = . . . . . .$ $c) . 6! 4! = . . .$ $d) . \frac{7!}{3!} \times \frac{2!}{5!} = . . . . . .$

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 ?

$h o w m a n y w a y s c a n y o u$ $e x c h a n g e 1 d o l l a r u s i n g$ $(1, 5, 10, 25, 50) c e n t s$ $e x a m p l e$ $1 d o l l a r (100 c e n t s) = 2 \times 50 c e n t s$ $= 1 \times 50 + 2 \times 25 = 4 \times 25$ $= 1 \times 50 + 1 \times 25 + 1 \times 10 + 1 \times 5 + 10 \times 1$ $a n d s o o n$ $h o w m a n y a l l t h e w a y s ?$

Question Number 156979 Answers: 2 Comments: 2

Question Number 155842 Answers: 1 Comments: 1

Prof that: Σ_(n=1) ^(10) n.n!=11!−1

$Prof that :$ $\underset{n = 1}{\sum^{10}} n . n! = 11! - 1$

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.

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

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 .

$Find the coefficient of term ‘ ‘ a^{m} b^{2 m}^{″} in {(1 + a)}^{m} {(1 + b)}^{n + m} {(1 + a + b)}^{m} .$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

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