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A letter lock consists of three rings marked with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then

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N

is product of 3 distinct prime numbers

N

is product of 4 distinct prime numbers

482 | N

none of these

answer is A, B.

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Detailed Solution

Since each ring has 15 position, the total number of attempts to open the lock is

15^{3}

ways out of these, there is one successful attempt

$∴ N = 15^{3} - 1 = 3375 - 1 = 3374 = 2.7.241$

Here $482 | N, N = 2.7.241$

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