Explanation
For 1 ≤ K ≤ p − 1, n + K = p! + K + 1 is clearly divisible by K + 1.
∴ there is no prime number in the given list.
105! + r is divisible by r for all r = 2, 3, ..., 105
∴ all the given numbers are composite numbers.
Hence (4) is correct.
Required number of ways 9! × 2.
[By fundamental property of circular permutation]
No. of ways in which 4 boys can be seated = (4 - 1)! = 3! = 6
Q Chairs of different colour = 4
∴ Total number of ways = 6 × 4 = 24.
Required number = (n – 1)!
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