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Q.

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

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An Intiative by Sri Chaitanya

a

$5! \times 6!$

b

$2! \times 3!$

c

6!

d

$5! \times 2 \times 3!$

answer is D.

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Detailed Solution

Question Image

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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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