Question

How many three​-digit numbers may be formed using elements from the set ​{1, 2, 3, 4, 5, 6, 7​} if no element may be used more than once in a number and the number must be​ even?

Answer 1

Answer: 90

Explanation:

set: ​{1, 2, 3, 4, 5, 6, 7​} = 7 numbers | 3 even

no element may be used more than once in a number = distinct elements

and the number must be​ even = must finish with a even number.

This way, we should start with the last number, which we have 3 possibilities.

Since we have 7 numbers in total, we have 6 options for the first one and then 5 options for the second one.

So, we have 6.5.3 = 90