A-delegation-of-4-students-is-to-be-selected-from-a-total-of-12-students-In-how-many-ways-can-the-delegation-be-selected-if-1-2-particular-students-wish-to-be-included-together-only-in-the-delegat

Question Number 50258 by rahul 19 last updated on 15/Dec/18

A d e l e g a t i o n o f 4 s t u d e n t s i s t o b e

s e l e c t e d f r o m a t o t a l o f 12 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 e d e l e g a t i o n

b e s e l e c t e d i f :

1) 2 p a r t i c u l a r s t u d e n t s w i s h t o b e

i n c l u d e d t o g e t h e r o n l y i n t h e d e l e g a t i o n ?

2) 2 p a r t i c u l a r s t u d e n t s r e f u s e t o b e

t o g e t h e r a n d 2 o t h e r p a r t i c u l a r s t u d e n t s

w i s h t o b e t o g e t h e r o n l y i n t h e d e l e g a t i o n ?

Answered by mr W last updated on 15/Dec/18

A, B a r e t h e t w o s t u d e n t s w h o w a n t

t o b e t o g e t h e r i n t h e d e l e g a t i o n .

C, D a r e t h e t w o s t u d e n t s w h o r e f u s e

t o b e t o g e t h e r i n t h e d e l e g a t i o n .

1)

w i t h A a n d B : C_{2}^{10} w a y s

w i t h o u t A a n d B : C_{4}^{10} w a y s

\Rightarrow C_{2}^{10} + C_{4}^{10} = 255 w a y s

2)

w i t h A a n d B : C_{2}^{10} - 1

t o s e l e c t t h e o t h e r t w o d e l e g a t e s f r o m

t h e o t h e r 10 s t u d e n t s, t h e r e a r e C_{2}^{10}

w a y s, b u t t h e s e l e c t i o n w i t h C a n d D

t o g e t h e r m u s t b e e x c l u d e d, t h e r e f o r e

t h e r e a r e o n l y C_{2}^{10} - 1 w a y s .

w i t h o u t A a n d B : C_{4}^{10} - C_{2}^{8}

a l l 4 d e l e g a t e s w i l l b e s e l e c t e d f r o m t h e

o t h e r 10 s t u d e n t s, t h e r e a r e C_{4}^{10} w a y s,

w i t h C a n d D t o g e t h e r t h e r e a r e C_{2}^{8}

w a y s w h i c h m u s t b e e x c l u d e d, t h e r e f o r e

t h e r e a r e o n l y C_{4}^{10} - C_{2}^{8} w a y s .

\Rightarrow C_{2}^{10} - 1 + C_{4}^{10} - C_{2}^{8} = 255 - 29 = 226 w a y s

Commented by rahul 19 last updated on 15/Dec/18

thank you sir!��