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Question: Answered & Verified by Expert
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
MathematicsPermutation CombinationWBJEEWBJEE 2023
Options:
  • A 482 divides \(\mathrm{N}\)
  • B N is the product of two distinct prime numbers.
  • C \(\mathrm{N}\) is the product of three distinct prime numbers.
  • D 16 divides \(\mathrm{N}\)
Solution:
2296 Upvotes Verified Answer
The correct answers are: 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

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