Answer:
The value is [tex]Z = 80[/tex]
Step-by-step 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
[tex]N = ^ nP_k[/tex]
Here P stands for permutation hence we are going to be making use of the permutation function in our calculators
[tex]N = ^ 5P_3[/tex]
=> [tex]N = 60[/tex]
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
[tex]M = ^ nP_a[/tex]
[tex]M = ^ 5P_2[/tex]
=> [tex]M = 20[/tex]
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
[tex]Z = M + N[/tex]
=> [tex]Z = 60 + 20[/tex]
=> [tex]Z = 80[/tex]
