Question

What is the number of ways that 5 boys and 4 girls can be seated in a row so that boys and girls sit alternately?
1. 1220
2. 2220
3. 2880
4. None of these

Answer 1

Correct Answer - Option 3 : 2880

Concept:

The number of permutations of n objects taken r at a time is given by

ⁿP_r = \(\rm \frac{n!}{(n - r)!}\)

where,

n = number of objects

r = number of positions

Calculation:

There can be only one arrangement in which boys and girls can sit.

B - G - B - G - B - G - B - G - B

But the position of individual boys and girls can be changed.

So, there are 5 boys and 5 slots for them that means they can be arranged in 5P5 or 5! ways,

similarly girls have 4 slots, so they can be arranged in 4P4 or 4! ways.

now, one more thing to consider is that out of 5! arrangements of boys, with each arrangement girls can be arranged in 4! different positions.

so to get the total number of boys and girls arrangements together we would need to multiply the arrangements of both boys and girls.

so the desired answer would be = ⁵P₅ \(\rm \times \) ⁴P₄ = 5! \(\rm \times \) 4! = 120 \(\rm \times \) 24 = 2880 ways.