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Question 63

The number of five-digit numbers, greater than 40000 and divisible by 5, which can be formed using the digits 0, 1, 3, 5, 7 and 9 without repetition, is equal to

Five-digit numbers > 40000, divisible by 5, using digits {0, 1, 3, 5, 7, 9} without repetition.

For divisibility by 5, the last digit must be 0 or 5.

Case 1: Last digit = 0

First digit ≥ 4: choices are {5, 7, 9} = 3 options

Remaining 3 positions: 4 × 3 × 2 = 24

Subtotal = 3 × 24 = 72

Case 2: Last digit = 5

First digit ≥ 4 and ≠ 5: choices are {7, 9} = 2 options

Remaining 3 positions from 4 remaining digits: 4 × 3 × 2 = 24

Subtotal = 2 × 24 = 48

Total = 72 + 48 = 120

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