Permutations Examples on Alphabets1

In this class, We discuss Permutations Examples on Alphabets1.

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

Example:

jagdise

1) Find the number of words that start with j and end with e.

Once we placed j in first position and e in last position.

The remaining five characters are filled in five positions in 5! Ways.

2) The number of words containing j and e on the extremes.

We can place j at the beginning and e at the end. Or vice-versa.

Two posible ways to fill j and e.

Total possibilities are 2 * 5!.

3) Find the number of words that contain vowels in even positions.

We have three vowels: a, e, and i.

We have three even positions: 2, 4, and 6.

The vowels can be placed in three positions in 3! ways.

The remaining four positions can be filled with four characters in 4! ways.

Total = 3! * 4!.

4) The number of words possible with j and e together.

j and e together mean we take je as a single element.

The order is not mentioned so that we can place je or ej.

2 posible ways to place je together.

Elements are je, a, g, d, i, and s.

Total = 2 * 6!

5) The number of ways that contain words j and e not together.

Words with j and e not together = Total words containing j and e together.

= 7! – 2* 6!.