First slide

Permutations

Question

The number of odd numbers lying between 40000 and 70000 that can be made from the digits 0, 1, 2, 4, 5, 7 if digits can be repeated in the same number is

Moderate

A

864
B

932
C

766
D

None of these

Solution

The numbers are of five digits having 4 or 5 in ten thousand’s place and 1 or 5 in unit’s place and the remaining digits are any of the given six digits.
∴ Number of ways to fill ten thousand’s place $=^{2} P_{1} = 2$
Number of ways to fill unit’s place $=^{2} P_{1} = 2$
Number of ways to fill other three places = 6³.
∴ Required number of numbers = 2 × 2 × 6³ = 864.

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