How many words can be formed from the letters of the word ‘SERIES’ which start with S and end with S?

Question

Philoid · Accepted Answer

Given the word SERIES. A total number of letters in it is 6. Two repeating characters S and E, both repeating twice.

To find: Total number of words that can be formed by permuting all digits in such a way that first place and the last will always be occupied by the letter S. For example- SRIEES, SERIES, SREIES are few words among them. Notice the first and last letter of the word is S.

Total number of such words can be formed by permutation of 4 letters (E, R, I, E) in between two S letters; which will be equals to

= 3 x 4

= 12

The denominator factor of 2! is because there is a repeating letter twice (E) in those 4 letters (E, R, I ,E).

Hence, a total number of words permuting the letters of the word SERIES in such a way that the first and last position is always occupied by the letter S is 12.