The number of nine digit numbers that can be formed with differen… - Vidyadip

MCQ

The number of nine digit numbers that can be formed with different digits is:

A
$9.8!$
B
$8.9!$
✓
$9.9!$
D
$10!$

✓

Answer

Correct option: C.

$9.9!$

The first digit is one of $(1, 2, 3, 4, 5, 6, 7, 8, 9) ($i.e., all expect $0).$
So, the no of ways $=9$
The remaining $8$ digits are to be taken from the remaining $9$ numbers.
So, the no of ways $= \ ^9\text{P}_8$
So, total no. of ways $=9\times\ ^9\text{P}_8$
$=9\times9!$

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