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Permutation and CombinationQuestion and Answers: Page 3

Question Number 195672 Answers: 2 Comments: 0

how many different words can be formed from the letters in aaacdefgbbbb such that a “a” and a “b” are not next to each other? (see also Q#195606)

$h o w m a n y d i f f e r e n t w o r d s c a n b e$ $f o r m e d f r o m t h e l e t t e r s i n$ $a a a c d e f g b b b b$ $s u c h t h a t a ‘ ‘ a^{″} a n d a ‘ ‘ b^{″} a r e n o t$ $n e x t t o e a c h o t h e r ?$ $You can't use 'macro parameter character #' in math mode$

Question Number 195538 Answers: 1 Comments: 7

Number of distributions of n different articles to r different boxes so as 1)empty box allowed 2)empty box not allowed with proof...kindly help me

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

Question Number 197578 Answers: 1 Comments: 1

Question Number 195015 Answers: 1 Comments: 0

Question Number 194960 Answers: 1 Comments: 0

Soit x>1. On de^ finie la suite (p_n ) par p_1 =x et ∀n∈IN^∗ p_(n+1) =2p_n ^2 −1 Montrer que lim_(n→+∞) Π_(k=1) ^n (1+(1/p_k ))=(√((x+1)/(x−1)))

$Soit x > 1 . On d \overset{´}{e f i n i e} la suite (p_{n}) par$ $p_{1} = x et \forall n \in {IN}^{*} p_{n + 1} = {2 p}_{n}^{2} - 1$ $Montrer que \lim_{n \to + \infty} \underset{k = 1}{\prod^{n}} (1 + \frac{1}{p_{k}}) = \sqrt{\frac{x + 1}{x - 1}}$

Question Number 194638 Answers: 1 Comments: 1

Prove that ∀n∈IN^∗ Σ_(k=1) ^(2^n −1) (1/(sin^2 (((kπ)/2^(n+1) ))))= ((2^(2n+1) −2)/3) Give in terms of n Σ_(k=1) ^(2^n −1) (1/(sin^4 (((kπ)/2^(n+1) ))))

$Prove that \forall n \in {IN}^{*}$ $\underset{k = 1}{\sum^{2^{n} - 1}} \frac{1}{{s i n}^{2} (\frac{k π}{2^{n + 1}})} = \frac{2^{2 n + 1} - 2}{3}$ $Give in terms of n \underset{k = 1}{\sum^{2^{n} - 1}} \frac{1}{{s i n}^{4} (\frac{k π}{2^{n + 1}})}$

Question Number 193864 Answers: 1 Comments: 0

Question Number 193368 Answers: 2 Comments: 0

If log_a y = (1/3) and log_8 a = x + 1 then show that y = 2^(x + 1)

$If \log_{a} y = \frac{1}{3} and \log_{8} a = x + 1 then show$ $that y = 2^{x + 1}$

Question Number 192960 Answers: 0 Comments: 0

Question Number 192256 Answers: 0 Comments: 0

given f(x)=cx(x−20) and A=(2,5) find the nearst point to A on the graph

$given f (x) = c x (x - 20) and A = (2, 5)$ $find the nearst point to A on the graph$

Question Number 191934 Answers: 1 Comments: 0

Question Number 191277 Answers: 0 Comments: 0

Question Number 190738 Answers: 0 Comments: 0

∫_0 ^( (π/2)) (((sin((x/2^n )))/(sinx))) dx , n ∈ N

$\int_{0}^{\frac{π}{2}} (\frac{s i n (\frac{x}{2^{n}})}{s i n x}) d x, n \in N$

Question Number 190602 Answers: 1 Comments: 0

let S={a,b,c,d,e,f} if we take any subset S (same subset is allowed), it also can be S, which will form S if we join them, order of operation does not matter ({a,b,c,d},{d,e,f}) is the same as ({d,e,f},{a,b,c,d}) how many ways can we choose?

$l e t S = {a, b, c, d, e, f}$ $i f w e t a k e a n y s u b s e t S (s a m e s u b s e t i s a l l o w e d),$ $i t a l s o c a n b e S, w h i c h w i l l f o r m S i f w e j o i n t h e m,$ $o r d e r o f o p e r a t i o n d o e s n o t m a t t e r$ $({a, b, c, d}, {d, e, f}) i s t h e s a m e a s$ $({d, e, f}, {a, b, c, d})$ $h o w m a n y w a y s c a n w e c h o o s e ?$

Question Number 190347 Answers: 1 Comments: 0

how is solution lim_(x→sinπ ) ((sin(π/2))/(sinx))=?

$h o w i s s o l u t i o n$ $\lim_{x \to \sin π} \frac{\sin \frac{π}{2}}{\sin x} = ?$

Question Number 190260 Answers: 1 Comments: 0

f : [1, 3] →R , f(x) = (1/x) A(1, 1) B(1, (1/3)) B′(b, (1/b)) , b ≥ 1 Find i. equation of line AB′ ii. equation of tangent T ′ to C_f at point with x = ((1 + b)/2) iii. Study relative positions of L_(AB ′) , T ′ to C_f

$f : [1, 3] \to R, f (x) = \frac{1}{x}$ $A (1, 1)$ $B (1, \frac{1}{3})$ $B^{'} (b, \frac{1}{b}), b ⩾ 1$ $F i n d$ $i . e q u a t i o n o f l i n e {A B}^{'}$ $i i . e q u a t i o n o f t a n g e n t T^{'} t o C_{f} a t p o i n t$ $w i t h x = \frac{1 + b}{2}$ $i i i . S t u d y r e l a t i v e p o s i t i o n s o f L_{A B^{'}}, T^{'} t o C_{f}$

Question Number 189614 Answers: 1 Comments: 0

Question Number 189049 Answers: 1 Comments: 2

Question Number 189021 Answers: 2 Comments: 4

How many non−similar triangles have integer angles in °?

$H o w m a n y n o n - s i m i l a r t r i a n g l e s$ $h a v e i n t e g e r a n g l e s i n ° ?$

Question Number 188551 Answers: 1 Comments: 0

you randomly select a 5 digit number. what′s the probability that this number has exactly 3 different digits?

$y o u r a n d o m l y s e l e c t a 5 d i g i t n u m b e r .$ ${w h a t}^{'} s t h e p r o b a b i l i t y t h a t t h i s n u m b e r$ $h a s e x a c t l y 3 d i f f e r e n t d i g i t s ?$

Question Number 188362 Answers: 2 Comments: 0

find the number of 5 digit natural numbers with strictly ascending digits whose sum is 20. example: 12458 is such a number

$f i n d t h e n u m b e r o f 5 d i g i t n a t u r a l$ $n u m b e r s w i t h s t r i c t l y a s c e n d i n g$ $d i g i t s w h o s e s u m i s 20 .$ $e x a m p l e : 12458 i s s u c h a n u m b e r$

Question Number 188301 Answers: 1 Comments: 4

Find the number of triangles with integer side lengths and perimeter p.

$F i n d t h e n u m b e r o f t r i a n g l e s w i t h$ $i n t e g e r s i d e l e n g t h s a n d p e r i m e t e r p .$

Question Number 187948 Answers: 1 Comments: 0

Given a set H={1,2,3,...,300. We will a create a subset of H consisting of three elements. If the sum of the three elements is divisible by 3 then the number of subsets that canbe made is x. Find the remainder if x is divided by 100000

$Given a set H = {1, 2, 3, . . ., 300 . We will a$ $cre a te a subset of H consisting of$ $thre e elements . If the sum of the$ $thr e e elements is divisible by 3$ $then the number of subsets that$ $canbe made is x . Find the$ $remaind e r if x is divided by 100000$

Question Number 185659 Answers: 1 Comments: 1

prove for r, n ∈ N Σ_(k=r) ^n ((k),(r) ) = (((n+1)),((r+1)) ) (Hockey−stick identity)

$p r o v e f o r r, n \in N$ $\underset{k = r}{\sum^{n}} (\begin{matrix} k \\ r \end{matrix}) = (\begin{matrix} n + 1 \\ r + 1 \end{matrix})$ $(H o c k e y - s t i c k i d e n t i t y)$

Question Number 185642 Answers: 1 Comments: 1

Question Number 185350 Answers: 0 Comments: 1

C_4 ^4 +C_4 ^5 +C_4 ^6 +...+C_4 ^(26) =?

$C_{4}^{4} + C_{4}^{5} + C_{4}^{6} + . . . + C_{4}^{26} = ?$

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