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Permutation and CombinationQuestion and Answers: Page 21

Question Number 36784 Answers: 0 Comments: 0

Prove that Σ_(r=0) ^n r ((n),(r) )^2 = n (((2n − 1)),(( n − 1)) )

$Prove that$ $\underset{r = 0}{\sum^{n}} r {(\begin{matrix} n \\ r \end{matrix})}^{2} = n (\begin{matrix} 2 n - 1 \\ n - 1 \end{matrix})$

Question Number 36398 Answers: 1 Comments: 1

Consider triangle ABC.If 206 lines are drawn from A to BC how many triangles are formed?

$C o n s i d e r t r i a n g l e A B C . I f 206$ $l i n e s a r e d r a w n f r o m A t o B C h o w$ $m a n y t r i a n g l e s a r e f o r m e d ?$

Question Number 35640 Answers: 1 Comments: 0

A panel of 3 women and 4 men is to be formed from 8 women and 7 men.Find the number of ways which the panel can be formed if it must contain at least 2 women.

$A p a n e l o f 3 w o m e n a n d 4 m e n i s$ $t o b e f o r m e d f r o m 8 w o m e n a n d$ $7 m e n . F i n d t h e n u m b e r o f w a y s$ $w h i c h t h e p a n e l c a n b e f o r m e d i f$ $i t m u s t c o n t a i n a t l e a s t 2 w o m e n .$

Question Number 35639 Answers: 0 Comments: 1

Three boys,two girls and a puppy sit at a round table.In how many ways can they be arranged if the puppy is to be seated i)between the two girls ii)between any two boys

$T h r e e b o y s, t w o g i r l s a n d a p u p p y$ $s i t a t a r o u n d t a b l e . I n h o w m a n y$ $w a y s c a n t h e y b e a r r a n g e d i f t h e$ $p u p p y i s t o b e s e a t e d$ $i) b e t w e e n t h e t w o g i r l s$ $i i) b e t w e e n a n y t w o b o y s$

Question Number 35348 Answers: 0 Comments: 0

Question Number 35347 Answers: 3 Comments: 0

Question Number 35344 Answers: 0 Comments: 0

Question Number 35165 Answers: 0 Comments: 2

In how many ways can a committee of 11 people be selected from 9 people.

$I n h o w m a n y w a y s c a n a c o m m i t t e e$ $o f 11 p e o p l e b e s e l e c t e d f r o m 9$ $p e o p l e .$

Question Number 35151 Answers: 1 Comments: 0

Question Number 34930 Answers: 1 Comments: 3

A committee of 4 is to be formed from 4 principals and 5 students.In how many ways can this be done if a particular student and a principal must be in the committee.

$A c o m m i t t e e o f 4 i s t o b e f o r m e d$ $f r o m 4 p r i n c i p a l s$ $a n d 5 s t u d e n t s . I n h o w m a n y w a y s$ $c a n t h i s b e d o n e i f a p a r t i c u l a r$ $s t u d e n t a n d a p r i n c i p a l m u s t b e$ $i n t h e c o m m i t t e e .$

Question Number 34878 Answers: 1 Comments: 0

show that C_(n−1) ^(n+r−1) =C_r ^(n+r−1)

$s h o w t h a t$ ${\overset{n + r - 1}{C}}_{n - 1} = {\overset{n + r - 1}{C}}_{r}$

Question Number 34877 Answers: 2 Comments: 1

4 couples are to take a photograph with a newly wedded couple in a wedding party.In how many ways can this be done if: i)the celebrated couple must stand in the middle ii)each couple must stand next to each other iii)the celebrated couple must not stand next to each other

$4 c o u p l e s a r e t o t a k e a p h o t o g r a p h$ $w i t h a n e w l y w e d d e d c o u p l e i n a$ $w e d d i n g p a r t y . I n h o w m a n y w a y s$ $c a n t h i s b e d o n e i f :$ $i) t h e c e l e b r a t e d c o u p l e m u s t s t a n d$ $i n t h e m i d d l e$ $i i) e a c h c o u p l e m u s t s t a n d n e x t t o$ $e a c h o t h e r$ $i i i) t h e c e l e b r a t e d c o u p l e m u s t n o t$ $s t a n d n e x t t o e a c h o t h e r$

Question Number 34410 Answers: 0 Comments: 0

Prove that (((n^2 )!)/((n!)^(n+1) )) is always an integer for n∈N.

$P r o v e t h a t \frac{(n^{2})!}{{(n!)}^{n + 1}} i s a l w a y s a n i n t e g e r$ $f o r n \in N .$

Question Number 32600 Answers: 0 Comments: 6

Question Number 32503 Answers: 0 Comments: 0

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$a l g e b r a 1 i c$

Question Number 32093 Answers: 1 Comments: 0

Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.

$F i n d t h e n u m b e r o f w a y s o f$ $s e l e c t i n g 9 b a l l s f r o m 6 r e d b a l l s,$ $5 w h i t e b a l l s a n d 5 b l u e b a l l s i f$ $e a c h s e l e c t i o n c o n s i s t s o f 3 b a l l s$ $o f e a c h c o l o u r .$

Question Number 31714 Answers: 0 Comments: 0

Prove that Σ_1 ^(n−2) k ((( n−2)),(( k)) ) (((n+2)),((k+2)) ) = (n−2) (((2n−1)),((n−1)) )

$Prove that$ $\underset{1}{\sum^{n - 2}} k (\begin{matrix} n - 2 \\ k \end{matrix}) (\begin{matrix} n + 2 \\ k + 2 \end{matrix}) = (n - 2) (\begin{matrix} 2 n - 1 \\ n - 1 \end{matrix})$

Question Number 31713 Answers: 0 Comments: 3

Given n ∈ N prove that Σ_(k=1) ^n k(n+1−k)= ((( n+2)),(( 3)) )

$Given n \in N$ $prove that$ $\underset{k = 1}{\sum^{n}} k (n + 1 - k) = (\begin{matrix} n + 2 \\ 3 \end{matrix})$

Question Number 28015 Answers: 1 Comments: 1

Question Number 27514 Answers: 1 Comments: 0

The president of a republic wishes to assign the premiership,the vice-premiership,and six other cabinet posts to a selected group of 8,comprising of 6 career diplomats and 2 business men.If none of the business men can be made premier or vice premier,in how many ways can the 8 posts be assigned to the 8 people?

$T h e p r e s i d e n t o f a r e p u b l i c w i s h e s$ $t o a s s i g n t h e p r e m i e r s h i p, t h e$ $v i c e - p r e m i e r s h i p, a n d s i x o t h e r$ $c a b i n e t p o s t s t o a s e l e c t e d g r o u p$ $o f 8, c o m p r i s i n g o f 6 c a r e e r$ $d i p l o m a t s a n d 2 b u s i n e s s m e n . I f$ $n o n e o f t h e b u s i n e s s m e n c a n b e$ $m a d e p r e m i e r o r v i c e p r e m i e r, i n$ $h o w m a n y w a y s c a n t h e 8 p o s t s$ $b e a s s i g n e d t o t h e 8 p e o p l e ?$

Question Number 27513 Answers: 1 Comments: 0

Using only the integers 4 to 8, how many even numbers can be formed if each must lie between 4000 and 9000?

$U s i n g o n l y t h e i n t e g e r s 4 t o 8,$ $h o w m a n y e v e n n u m b e r s c a n b e$ $f o r m e d i f e a c h m u s t l i e b e t w e e n$ $4000 a n d 9000 ?$

Question Number 27270 Answers: 0 Comments: 0

(1) There are 20 boys and 10 girls in a class.If a committee of 6 is to be chosen at random having atleast 2 boys and 2 girls,find the probability that (i) there ara 3 boys in the committee (ii) there are 4 boys in the committee

$(1) There are 20 boys and 10 girls in a$ $class . If a committee of 6 is to be$ $chosen at random having atleast$ $2 boys and 2 girls, find the$ $probability that$ $(i) there ara 3 boys in the$ $committee$ $(ii) there are 4 boys in the$ $committee$

Question Number 26732 Answers: 0 Comments: 1

Question Number 26555 Answers: 0 Comments: 1

(2) Find the 10th trem in the expansion of (2x−(y/2))

$(2) Find the 10 th trem in the$ $expansion of (2 x - \frac{y}{2})$

Question Number 26554 Answers: 1 Comments: 0

(2) Find the middle trem(s) in the expansion of following− (x^2 +(1/x^3 ))^(14)

$(2) Find the middle trem (s) in the$ $expansion of following -$ ${(x^{2} + \frac{1}{x^{3}})}^{14}$

Question Number 26480 Answers: 1 Comments: 0

Find the number of all possible different words into which the word INTERFERE can be converted by change of place of letters,if no two consonants must be together.

$F i n d t h e n u m b e r o f a l l p o s s i b l e$ $d i f f e r e n t w o r d s i n t o w h i c h t h e$ $w o r d I N T E R F E R E c a n b e$ $c o n v e r t e d b y c h a n g e o f p l a c e o f$ $l e t t e r s, i f n o t w o c o n s o n a n t s$ $m u s t b e t o g e t h e r .$

Pg 16 Pg 17 Pg 18 Pg 19 Pg 20 Pg 21 Pg 22 Pg 23 Pg 24 Pg 25

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