To construct one three-digit number and one two-digit number from 1,2,3,4,5 without using any number twice, what’s the probability of getting two even numbers?

Answer 1

First determine the total outcomes.

There are 60 three digit numbers (5 * 4* 3).

For each of these three digit number there are 2 two digit numbers.

That make a total of 120 possible numbers.

There are 6 possible two digit even numbers

12, 14, 32, 34, 52, 54

For each two digit even number there are 2 three digits evens

E.g.

12 - 354, 534

14 - 352, 532

6 times 2 is 12.

The probability is 12/120, or 1/10.