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The number of `6` digit numbers that can be made with the digits `1, 2, 3` and `4` and having exactly two pairs of digits, isA. 480B. 540C. 1080D. none of these |
Answer» The number of 6-digits has two pairs of digits and 2 different digits. The number of ways of selecting 2 digits for two pairs and 2 other digits `=""^(4)C_(2)xx""^(2)C_(2)`. Now, we arrange these six digits which consists of two pairs and 2 different digits. This can be done in `(6!)/(2!2!)` ways. `:.` Required numbers `=""^(4)C_(2)xx""^(2)C_(2)xx(6!)/(2!2!)=1080`. |
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