There are 5 boys and 3 girls. In how many ways can they stand in a row

1.	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» (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

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»

(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