100-students-are-standing-in-a-row-4-students-should-be-selected-in-the-way-that-no-two-of-them-are-next-to-each-other-how-many-ways-do-you-have-to-do-this-

Question Number 103406 by mr W last updated on 16/Jul/20

100 s t u d e n t s a r e s t a n d i n g i n a r o w .

4 s t u d e n t s s h o u l d b e s e l e c t e d i n t h e

w a y t h a t n o t w o o f t h e m a r e n e x t t o

e a c h o t h e r . h o w m a n y w a y s d o y o u

h a v e t o d o t h i s ?

Commented by bobhans last updated on 15/Jul/20

n (S) = C_{4}^{100} = \frac{100!}{4! . 96!}

n (A) = 100! - 50 . C_{2}^{50} = 100! - 50 \times \frac{50!}{2! . 48!}

p (A) = \frac{100! - 50 . \frac{50!}{2.48!}}{100!} \times 4! . 96!

= \frac{100! - \frac{50.50!}{2.48!}}{100.99.98.97} \times 4! = \frac{100! - \frac{50.50.49}{2}}{100.99.98.97} \times 4!

Commented by mr W last updated on 16/Jul/20

3 464 840 w a y s

Commented by mr W last updated on 16/Jul/20

a n s w e r s e e Q 103716

Facebook Tweet Pin