# How many 9-digit numbers of different digits can be formed?

Question:

How many 9-digit numbers of different digits can be formed?

Solution:

Since the first digit cannot be zero, number of ways of filling the first digit = 9

Number of ways of filling the second digit = 9    (as repetition is not allowed or the digits are distinct)

Number of ways of filling the third digit = 8

Number of ways of filling the fourth digit = 7

Number of ways of filling the fifth digit = 6

Number of ways of filling the sixth digit = 5

Number of ways of filling the seventh digit = 4

Number of ways of filling the eighth digit = 3

Number of ways of filling the ninth digit = 2

Total such 9-digit numbers $=9 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2=9(9 !)$