First slide

Permutations

Question

The sum of all the numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time is

Moderate

A

66666
B

84844
C

93324
D

None of these

Solution

The total number of numbers that can be formed with the digits 2, 3, 4, 5 taken all at a time $=^{4} P_{4} = 4! = 24$ . Consider the digit in the unit’s place in all these numbers. Each of the digits 2, 3, 4, 5 occurs in 3! = 6 times in the unit’s place
$∴$ total for the digits in the unit’s place = (2 + 3 + 4 + 5) 6 = 84
Since each of the digits 2, 3, 4, 5 occurs 6 times in any one of the remaining places
$∴$ the required total = 84 (1 + 10 + 10² + 10³) = 84 (1111) = 93324.

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