Permutations Examples on Numbers1

In this class, We discuss permutation examples on Numbers1.

The reader should have prior knowledge of permutation formulae. Click here.

Examples:

Given 0, 1, 2, 4, 7, and 9.

1) How many four-digit numbers are possible?

We need four-digit numbers, so we have four positions.

The above digits contain zero.

The first position should be filled with something other than zero.

We have five elements to be filled in the first position.

The second position can be filled with five digits.

The third position can be filled with four digits and so on.

Total possibilities are 5 * 5 * 4 * 3 = 300

2) How many four-digit even numbers are possible?

The last position can be filled with 0, 2, or 4 to make an even number.

Placing zero and non-zero in the last case can be identified separately.

By placing zero in the last position, the number of permutations is 5p3.

The number of permutations by placing 2 or 4 in the last position is 2 * 4 * 4p2.

Total = 60 + 96 = 156

3) How many four-digit numbers are divisible by 5?

We can place 0 or 5 in the last position to divide the number by 5.

Find the permutations for both cases separately.

Total = 60 + 48 = 108