The number of all numbers having 5 digits, with distinct digits is

Question

The number of all numbers having 5 digits, with distinct digits is (A) 99999 (B) 9 × 9P4 (C)  10P5 (D)  9P4

Tardigrade Admin · Accepted Answer

Total number of 5 -digit numbers having all the digits distinct = 10 P 5- 9 P4 =(10 !/5 !)-(9 !/5 !)=(10 × 9 !/5 !)-(9 !/5 !) =(9 !/5 !)(10-1)=(9 !/(9-4) !)(9) =9 × 9 P4

Q. The number of all numbers having $5$ digits, with distinct digits is

$99999$

$9 \times^{9} P_{4}$

$^{10} P_{5}$

$^{9} P_{4}$

Total number of $5$ -digit numbers having all the digits distinct $=^{10} P_{5} -^{9} P_{4}$
$= \frac{10 !}{5 !} - \frac{9 !}{5 !} = \frac{10 \times 9 !}{5 !} - \frac{9 !}{5 !}$
$= \frac{9 !}{5 !} (10 - 1) = \frac{9 !}{( 9 - 4 )!} (9)$
$= 9 \times^{9} P_{4}$

Q. The number of all numbers having 5 digits, with distinct digits is

99999

9×9P4​

10P5​

9P4​