Question

There are 5 boys and 3 girls. In how many ways can they stand in a row so that no two girls are together?

(a) 36000 

(b) 25600 

(c) 14400 

(d) 15600

Answer 1

(c) 144000

First of all we arrange the 5 boys in 5 ! ways. 

Then we arrange the 3 girls in the remaining 6 places between the 5 boys and on the extreme in ⁶P₃ ways. 

× B × B × B × B × B × 

∴ Required number of ways = 5 ! × ⁶P₃ 

= 120 × 6 × 5 × 4 = 144000