# How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5

Question:

How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?

Solution:

The first digit cannot be zero. Thus, the first digit can be filled in 5 ways.

Number of ways for filling the second digit = 5    (as repetition of digits is not allowed)

Number of ways for filling the third digit = 4

Number of ways for filling the fourth digit = 3

Number of ways for filling the fifth digit = 2

Number of ways for filling the sixth digit = 1

Total numbers $=5 \times 5 \times 4 \times 3 \times 2 \times 1=600$