How many 4-digit numbers are there with no digit repeated? - Vidyadip

Question

How many 4-digit numbers are there with no digit repeated?

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Answer

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.
$\therefore $ Number of permutations = $^9{P_3}$
$= \frac{{9!}}{{6!}} = \frac{{9 \times 8 \times 7 \times 6!}}{{6!}} = 504$
Hence total number of permutations $= 9 \times 504 = 4536$

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