Question

In how many ways can 3 boys and 2 girls be arranged In a row such that.

(I) both the girls remain together?
(II) boys and girls are alternately arranged?
(III) all the three boys remain together?

Answer 1

3 boys and 2 girls are to be arranged in a row.

(i) Both the girls remain together:

∴ Total permutations in which both the girls remain together ⁴P₄ × ²P₂
= 4! × 2!
= 24 × 2 = 48

(ii) Boys and girls are alternatively arranged:

∴Total permutations in which boys and girls are alternatively arranged
³P₃ × ²P₂
= 3! × 2!
= 6 × 2
= 12

(iii) All the there boys remain together:

∴ Total permutations in which all the three boys remain to gether = ³P₃ × ³P₃
= 3! × 3!
= 6 × 6
= 36