Question

An identification code is to consist of 2 letters followed by 3 digits. how many different codes are possible if repetition is not permitted

Answer 1

(26^2)*(10^3)
676*1000
676,000 possibilities

Answer 2

11232000

Explanation:

Given that an identification code is to consist of 2 letters followed by 3 digits.

Also given that repetition is not permitted.

Since order matters here we find that permutation to be used.

Out of 26 letters, 2 letters can be selected without repitition in
`26P2` ways

And 3 codes can be selected from 10 digits in
`10P3` ways

Hence total number of codes =
`10P3(26P2)\\\\=10(9)(8) (26)(25)(24)\\=720(100)(156)\\=11232000`

No of ways = 11232000