Question

How many anagrams are there to the word FRIDAY? In how many of these do the letters 'DAY' appear consecutively? (Disregard whether the word actually exists in the dictionary or can even be pronounced)

Answer 1

There are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.

Explanation:

FRIDAY is a six letter word.

To form all combinations of letters, we would have six choices of letters to fill the first spot. Whatever letter you choose for the first spot, you then have five choices of letters to fill the second spot. Four choices of letters to fill the third spot. And so on.

So, the total number of different combinations of the six letters would be 6!

6! = 6 X 5 X 4 X 3 X 2 X 1

   = 720

DAY could appear consecutively starting in 4 different spots: the 1st, 2nd, 3rd, and 4th spots of all combinations. DAY will appear consecutively 6 times in each of those 4 starting spots.

6 X 4 = 24.

So, there are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.