The number of four-digit numbers that can be formed by using the digits `1,2,3,4,5,6,7,8` and `9` such that the least digit used is `4`, when repetition of digits is allowed is

Options

A. `617`
B. `671`
C. `716`
D. `761`

Answer

B

Explanation

`(b)` Least digit used `=4`
`:.` We can use `4,5,6,7,8,9`.
So each of the four places can be filled in `6` ways
So number of numbers is `6^(4)`
But many numbers may not contain `4`
Number of numbers not containing `4` is `5^(4)` (as each place can now be filled in `5` ways)
So, required number of ways `=6(4)-5^(4)`(at least one `4`)