Four students of class X, five students of class XI and six students of class XII sit in a row. The number of ways, they can sit in a row so that students belonging to the same class are together is :

Question

Four students of class X, five students of class XI and six students of class XII sit in a row. The number of ways, they can sit in a row so that students belonging to the same class are together is : (A) 3! 4! 5! 6! (B) 3 × 4! 5! 6! (C) 4! 5! 6! (D) (15!/4! 5! 6!)

Tardigrade Admin · Accepted Answer

Treating them as three groups, the three groups can be arranged in 3! ways. There after each group can be arranged internally. Total number = 3! × 4! × 5! × 6!

Q. Four students of class X, five students of class XI and six students of class XII sit in a row. The number of ways, they can sit in a row so that students belonging to the same class are together is :

3! 4! 5! 6!

3 $\times$ 4! 5! 6!

4! 5! 6!

$\frac{15 !}{4 ! 5 ! 6 !}$

Treating them as three groups, the three groups can be arranged in 3! ways. There after each group can be arranged internally.
Total number = 3! $\times$ 4! $\times$ 5! $\times$ 6!