MathematicsIn how many different ways can five boys and five girls form a circle such that the boys and girls alternate?

In how many different ways can five boys and five girls form a circle such that the boys and girls alternate?

A
$2880$
B
$2888$
C
$28809$
D
None

Solution:

After fixing up one boy on the table, the remaining can be arranged in $4!$ ways but boys and girls are to alternate. There will be $5$ places, one place each between two boys these five places can be filled by $5$ girls in $5!$ ways.

Hence, by the principle of multiplication, the required number of ways $= 4! \times 5! = 2880 .$

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