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Q.

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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a

482|N

b

N  is product of 3 distinct prime numbers

c

N  is product of 4 distinct prime numbers

d

none of these

answer is B, A.

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Detailed Solution

Since each ring has 15 position, the total number of attempts to open the lock is 153  ways out of these, there is one successful attempt

∴N=153−1=3375−1=3374=2.7.241

Here 482|N, N=2.7.241

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