JEE MAIN - Mathematics (2023 - 8th April Morning Shift - No. 6)
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 :
720
$$7(360)^{2}$$
$$7(720)^{2}$$
$$126(5 !)^{2}$$
Explanation
We have,
Number of girls $=5$
Number of boys $=7$
_8th_April_Morning_Shift_en_6_1.png)
So, number of ways of arranging boys
around the table $=6$ ! and 5 girls can be arranged in 7 gaps in ${ }^7 \mathrm{P}_5$ ways.
$\therefore$ Required no. of ways $=6 ! \times{ }^7 \mathrm{P}_5$ $=126 \times(5 !)^2$
Number of girls $=5$
Number of boys $=7$
So, number of ways of arranging boys
around the table $=6$ ! and 5 girls can be arranged in 7 gaps in ${ }^7 \mathrm{P}_5$ ways.
$\therefore$ Required no. of ways $=6 ! \times{ }^7 \mathrm{P}_5$ $=126 \times(5 !)^2$
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