CUET UG 2025 — General Test Quantitative Reasoning

When people sit around a round table, rotations look the same. If everyone shifts one seat clockwise, it's still the same arrangement. For $n$n people at a round table, there are $(n-1)!$(n−1)! arrangements (not $n!$n!).

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First, decide which people sit at which table: 7 people go to the 7-seater table and 8 people go to the 8-seater table.

Number of ways to choose 7 people from 15:

$$\dfrac{15!}{7! \times 8!}$$7!×8!15!​

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For the round table with 7 people, the number of arrangements is:

$$(7-1)! = 6!$$(7−1)!=6!

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For the round table with 8 people, the number of arrangements is:

$$(8-1)! = 7!$$(8−1)!=7!

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Total number of ways:

$$= \dfrac{15!}{7! \times 8!} \times 6! \times 7!$$=7!×8!15!​×6!×7!

$$= \dfrac{15! \times 6! \times 7!}{7! \times 8!}$$=7!×8!15!×6!×7!​

$$= \dfrac{15! \times 6!}{8!}$$=8!15!×6!​

$$= \dfrac{15!}{8!} \times 6!$$=8!15!​×6!

Therefore, the answer is $\dfrac{15!}{8!} \times 6!$8!15!​×6!