Five boys and five girls form a line with the boys and girls alternating. Find the number of ways of making the line.

Options

A. `(5!)^(2)`
B. `10!`
C. `5!+5!`
D. `2(5!)^(2)`

Answer

D

Explanation

5 boys can be arranged in a linen in 5! Ways. Since the boys and girls are alternating. So, corresponding each of the 5! Ways of arrangements of 5 boys we obtain 5 places marked by cross as shown below:
(i) `B_(1)xxB_(2)xxB_(3)xxB_(4)xxB_(5)` (ii) `xxB_(1)xxB_(2)xxB_(3)xxB_(4)xxB_(5)`
Clearly, 5 girls can be arranged in 5 places marked by cross in `(5!+5!)` ways.
Hence, the total number of ways of making the line
`=5!xx(5!+5!)=2(5!)^(2)`