MathematicsThere are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that every gentleman have a lady on this adjacent

There are 6 gentlemen and 3 ladies to dine at a round table. In how many ways can they seat themselves so that every gentleman have a lady on this adjacent

A
6!
B
$2! \times 3!$
C
$5! \times 6!$
D
$5! \times 2 \times 3!$

Solution:

Gentlemen can be arranged in 5! Ways. Now ladies have occupied 1, 3, 5 positions (or) 2, 4, 6 positions

Hence total $= 5! \times 2 \times 3!$

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