Suppose you have a word EXAMINATION a How many 11letter word

Suppose you have a word E-X-A-M-I-N-A-T-I-O-N.
a. How many 11-letter words can you create?

b. How many 11-letter words starting with letter X can you create?

c. How many 10-letter words can you create?

d. How many 10-letter words starting with letter A can you create?

Solution

a) 11! / (2! * 2! * 2! ) = 4989600

b) 10!/ (2! * 2! * 2! ) = 453600

c) There is a bijection between the 10-letter words that can be formed and the 11-letter words, given by appending the one remaining letter to the end of the 10-letter word. Therefore, the total number of 10-letter words is simply

= 4989600

d) 9! / (2!*2!) = 90720