Visual SolutionPYQ 2023 · Apr 8 Shift 1Tricky

Question

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)

720

(B)

126(5!)^2

(C)

7(360)^2

(D)

7(720)^2

Solution Path

Gap method:

6! \times {}^{7}C_{5} \times 5! = 126(5!)^2

01Question Setup

1/4

5 girls and 7 boys at a round table, no two girls sit together.

\text{Ways} = \;?

02Seat Boys First

2/4

Boys in circle:

(7-1)! = 6!

ways. Creates 7 gaps. Choose 5 gaps for girls:

{}^{7}C_{5} = 21

6! \times {}^{7}C_{5}

03MultiplyKEY INSIGHT

3/4

Total

= 6! \times 21 \times 5! = 6 \cdot 5! \times 21 \times 5! = 126(5!)^2

126(5!)^2

04Final Answer

4/4

Number of ways

= 126(5!)^2

\boxed{126(5!)^2}

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