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A letter lock consists of three rings with 15 different letters. If \(\mathrm{N}\) denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then
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482 divides \(\mathrm{N}\), \(\mathrm{N}\) is the product of three distinct prime numbers.
Hint : Number of unsuccessful attempts \(=15^3-1=3374=2 \times 1687=2 \times 7 \times 241\)
Divisible by 482
\(\mathrm{N}\) is the product of three distinct prime number
Divisible by 482
\(\mathrm{N}\) is the product of three distinct prime number
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