Question

A license plate is to consist of 5 digits followed by 5 uppercase letters. Determine the number of different license plates possible if the first and second digits must be​ odd, and repetition is not permitted.

Answer 1

`5.3044992* 10^(10)`

Explanation:

We are given that a license plate consist of 5 digits and 5 uppercase letters

Digits used=0,1,2,..9

Total number of letters=26

Repetition is not allowed

Total number of odd digits=(1,3,5,7,9)=5

The first place filled by 5

Second place filled by 4

Third place filled by 8

Fourth place filled by 7

Fifth place filled by 6

Sixth place filled by 26

Seventh place filled by 25

Eighth place filled by 24

Ninth place filled by 23

Tenth place filled by 22

Total number of possible different license plates =
`5* 4* 8* 7* 6* 26* 25* 24* 23* 22`=
`5.3044992* 10^(10)`