Permutations with Repetitions Examples on Numbers1

In this class, We discuss Permutations with Repetitions Examples on Numbers1.

The reader should have prior knowledge of permutations with repetitions formulae. Click Here.

Examples:

The numbers are 2, 3, 6, 6, 7.

1) Total permutations possible with the given numbers?

Five digits are placed in five positions.

Two digits are repeated.

Total permutations are 5!/2!

2) Total even numbers possible?

The last position can be filled with 2 or 6 to make an even number.

The two numbers’ permutations are found separately. Because 6 is repeated.

Placing 2 in the last position.

The permutations are 4!/2!. Because 6 is repeated.

Placing 6 in the last position.

The permutations are 4! Because there are no repeated elements.

Total permutations are 4!/2! + 4!.

3) Total odd numbers possible.

The last position should be filled with 3 or 7 for odd numbers.

Placing 3 or 7 in the last position is done in 2 ways.

Total permutations are 2 * 4!/2!.

4) Even digits occupy odd places.

2, 6, and 6 occupy odd places 1, 3, and 5.

even numbers permutations are 3!/2!

The remaining 2 positions are filled with 2 numbers in 2! ways.

Total permutations are 3!/2! * 2!.