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in Mathematics by (79.8k points)

Five digit numbers are formed with 0, 1, 3, 5, 7. The number of numbers in which at least one digit is repeated is 

(1) 96 

(2) 2400 

(3) 2500 

(4) 2404

1 Answer

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Best answer

Correct option (4) 2404

Explanation: 

The number of all five digit numbers that can be formed with 0, 1, 3, 5,7 = 4.54

(∴ 0 cannot occur in the 10000th place)

= 2500

The number of numbers without any repetition 

= 4 × 4 × 3 × 2 × 1 = 96

∴ the number of five digit numbers with at least one digit repeated 

= 2500 − 96 = 2404

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