Puzzle 18) Number Plates of Defence colony

Puzzle

A new defence colony is constructed in defence area. The builder of defence area is suffering from a problem that he doesn’t know that How many house number plates in a newly constructed defence colony can be made, if the no. plates have two letters of English alphabet followed by a two- digit no., if repetition of digits or alphabets is not allowed? He asked you to solve this problem. Now your task is to find out number of number plates which builder can create by applying above conditions.

Important points of puzzle:

1. A new defence colony is constructed in defence area.
2. Builder have a problem.
3. He doesn’t know that how many house number plates in a newly constructed defence colony can be made?
4. If the no. plates have two letters of English alphabet followed by a two- digit no., if repetition of digits or alphabets is not allowed.
5. Now your task is to find out number of number plates which builder can create by applying above conditions.

Answer

58500

Reason

The alphabets have to be arranged by selecting 2 from 26 and arranging them. Also, 2 digits out of 10 digits have to be arranged ²⁶P₂ *¹⁰P₂ = 58500. Hence, the correct answer is 58500.