Number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit

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6.Permutation and Combination

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The number of ways, in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together, is

A

$126(5 !)^2$

B

$7(360)^2$

C

$720$

D

$7(720)^2$

(JEE MAIN-2023)

Solution

$6 ! \times{ }^7 C_5 \times 5 !$

$\Rightarrow 720 \times 21 \times 120$

$\Rightarrow 2 \times 360 \times 7 \times 3 \times 120$

$\Rightarrow 126 \times(5 !)^2$

Standard 11

Mathematics

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