How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?

i don’t have any prior experience to deal with this kind of problem.

=================

1

Hint: Remove one E and one R, and find out how many two letter words can be formed from the rest.

– true blue anil

2 days ago

=================

2 Answers

2

=================

It equivalent to choosing two distinct letters (with order mattering) from the word Mditeranean\textit{Mditeranean}

Be careful not to double count ‘ee’ ‘aa’ or ‘nn’

– SquirtleSquad

2 days ago

Removing E and R from MEDITERRANEAN, we are left with:

11 M

11 D

11 I

11 T

11 R

22 As

22 Es

22 Ns

From which we need to choose any 22 letters in any order.

There are 33 sequences containing the same letter (AA, EE, NN).

Given 88 different letters, there are (82)⋅2!=56\binom82\cdot2!=56 sequences containing 22 different letters.

Hence the total number of 44-letter words starting with E and ending with R is 3+56=593+56=59.