Choose the correct answer. The total number of 9 digit numbers wh… - Vidyadip

MCQ

Choose the correct answer. The total number of $9$ digit numbers which have all different digits is.

A
$10!$
B
$9 !$
✓
$9 \times 9!$
D
$10\times 10!$

✓

Answer

Correct option: C.

$9 \times 9!$

We have to form $9-$digit number which has all different digit.
First digit from the left can be filled in $9$ ways $($excluding $'0\ ').$
Now nine digits are left including $'O\ '.$
So remaining eight places can be filled with these nine digits in ${ }^9 P_S$ ways.
So, total number of numbers $=9 \times{ }^9 \mathrm{P}_8=9 \times 9$ !

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