Question

How many different four letter words can be formed (with or with out meaning) using the letters of the word “MEDITERRANEAN” such that the first letter is E and the last letter is R.

Answer 1

We should complete word E_ _ R using set {M-1, E-2 (one E we use as the first letter), D-1, I-1, T-1, R-1 (one R we use as the last letter), A-2, N-2}

So, the set consist of 5 single letters and 3 pairs of letters. 

Case 1. For third position we have 8 cases (or 5 + 3) 

Case 2. For third position we have either 8 cases (second letter is from a pair) or 7 cases (second letter is single letter). 

Therefore, number of different words = 3 × 8 × 5 × 7 

= 24 + 35 = 59