Question

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

Answer 1

60

Explanation:

A 3-digit number can be odd only when the third digit in it would be odd.

So,

The 3rd digit becomes the most limiting which can be (1, 3, or 5).

Now,

Since we have 3 alternatives to pick the third digit, it can be done in three ways. For every of these 3 ways, 5 digits will be left to select the 1st. Thus, the number of ways to select 3rd and 1st digit = 3 * 5 = 15 ways

After picking the 1st and 3rd digits, we are left with 4 ways to pick the other 4 digits. Thus, the total number of ways to select all the digits would be;

3 * 5 * 4 = 60 ways

Hence, 60 is the correct answer.