How many different four letter words can be formed using the letters of the word MEDITERRANEAN

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

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

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’
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.