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How many 4 digit number are there with no digit repeated

Posted by Nitin Parihar 2 years, 1 month ago

MP Board > Class 11 > Mathematics

1 answers

Preeti Dabral 2 years, 1 month ago

Here total number of digits = 10
Number of digits used (no digit is repeated) = 4
Since 0 cannot be filled in the fourth place, so number of permutations for fourth place = 9
Now the remaining three places can be filled with 9 digits.
{tex}\therefore {/tex} Number of permutations = {tex}^9{P_3}{/tex}
{tex}= \frac{{9!}}{{6!}} = \frac{{9 \times 8 \times 7 \times 6!}}{{6!}} = 504{/tex}
Hence total number of permutations {tex}= 9 \times 504 = 4536{/tex}

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MP Board > Class 11 > Mathematics