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| 1. |
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 |
| Answer» <p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong>Correct option (4) 2404</strong></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif"><strong>Explanation: </strong></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">The number of all five digit numbers that can be formed with 0, 1, 3, 5,7 = 4.5<sup>4</sup></span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">(∴ 0 cannot occur in the 10000<sup>th</sup> place)</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">= 2500</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">The number of numbers without any repetition </span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">= 4 × 4 × 3 × 2 × 1 = 96</span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">∴ the number of five digit numbers with at least one digit repeated </span></span></p><p style="text-align: justify;"><span style="color:#000000"><span style="font-family:Arial,Helvetica,sans-serif">= 2500 − 96 = 2404</span></span></p><p></p> | |