Question

A door lock requires 3 different letters to be pressed in the correct order. If each permutation can only be made from the letters ABC, how many different permutations can there be?

Answer 1

ABC ACB BAC BCA CBA CAB
total:6

Answer 2

Answer: 6 different permutations .

Explanation:

The permutation of n things taken r at a time is given by:-

`^nP_r=(n!)/((n-r)!)`

Given : A door lock requires 3 different letters to be pressed in the correct order.

If each permutation can only be made from the letters ABC, then the number of different permutations can there be is given by :-

`^3P_3=(3!)/((3-3)!)=3!=3*2=6`

Hence, there can be 6 different permutations .