How many different ways are there to arrange the 6 letters in the word SUNDAY?

1 Answer
Dec 19, 2016

Answer:

There are 720 different ways to arrange the 6 letters in SUNDAY.

Explanation:

The first letter of the rearrangement can be any 1 of 6 letters.

The second letter can now be any 1 of 5 letters. So the first two letters can be a combination of #color(red)(6 xx 5)# letters or #color(red)(30)# arrangements.

The third letter can be any 1 of 4 remaining letters. So the first three letters can be a combination of #color(red)(6 xx 5 xx 4)# letters or #color(red)(120)# arrangements.

The fourth letter can now be any 1 of 3 remaining letters. So the first four letters can be a combination of #color(red)(6 xx 5 xx 4 xx 3)# letters or #color(red)(360)# arrangements.

The fifth letter can now be only 1 of 2 remaining letters. So the first five letters can be a combination of #color(red)(6 xx 5 xx 4 xx 3 xx 2)# letters or #color(red)(720)# arrangements.

The final letter can now be only 1 letter because all of the others have been used. So the six letters can be a combination of #color(red)(6 xx 5 xx 4 xx 3 xx 2 xx 1)# letters or #color(red)(720)# arrangements.