First slide

Permutations

Question

The number of natural numbers less than $7, 000$ which can be formed by using the digits $0, 1, 3, 7, 9$ (repetition is allowed) is equal to

Moderate

A

250
B

374
C

372
D

375

Solution

Thousands place can be filled in 3 ways and each of the remaining places can be filled in 5 ways. Hence, required number of natural numbers is
$3 \times 5 \times 5 \times 5 - 1 = 374$

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