Permutation Examples on Numbers

In this class, we discussed permutation examples on numbers.

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

Example:

Consider the six digits 1, 2, 3, 5, 6, and 7.

Assume repetition is not permitted.

1) How many four-digit numbers can be formed?

Six digits can be placed in four positions in 6p4 ways.

N = 6 and r = 4.

6p4 = 6!/(6-4)!

= 360

2) How many numbers are less than 4000?

If we need to form four-digit numbers less than 4000. we take 1, 2, or 3 in the first position.

The numbers starting with 1, 2, or 3 are less than 4000.

The first position can be filled in three ways.

The remaining three positions can be filled in 5p3 ways.

Total permutations = 3 * 5p3 possible ways.

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

The last position should be filled with even numbers to find even numbers.

2 and 6 are even numbers available.

The last position can be filled in two ways.

The remaining three positions can be filled in 5p3 ways.

Total = 2 * 5p3

4) How many four-digit numbers contain 5 and 7?

5 and 7 can take any four positions.

5 and 7 can be filled in 4p2 ways.

The remaining two positions can be filled in 4p2 ways.

Total = 4p2 * 4p2

= 144.