Question

How many 5-digit numbers are there in which three of the digits are 6, or two of

the digits are 9 ?

Answer 1

The value is
`Z = 80`

Explanation:

From the question we are told that

The total number of digit is n = 5

The total possible number of 6 is k = 3

The total possible number of 9 is a = 2

Generally the number of way of representing a 5 digits number(i.e the number of five digit numbers ) in which 3 of the digit are 6 is mathematically represented as

`N = ^ nP_k`

Here P stands for permutation hence we are going to be making use of the permutation function in our calculators

`N = ^ 5P_3`

=>
`N = 60`

Generally the number of way of representing a 5 digits number(i.e the number of five digit numbers ) in which 2 of the digit are 9 is mathematically represented as

`M = ^ nP_a`

`M = ^ 5P_2`

=>
`M = 20`

Generally the number of 5-digit numbers there are in which three of the digits are 6, or two of the digits are 9 is mathematically represented as

`Z = M + N`

=>
`Z = 60 + 20`

=>
`Z = 80`