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perm&comb, prob...

by romitvsingh » Wed Nov 23, 2011 10:20 pm
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?

A. 59

B. 11!/2!*2!*2!

C. 56

D. 23

E. 11!/3!*2!*2!*2!
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by Anurag@Gurome » Wed Nov 23, 2011 11:30 pm
romitvsingh wrote: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?

A. 59

B. 11!/2!*2!*2!

C. 56

D. 23

E. 11!/3!*2!*2!*2!
No. of letters in "MEDITERRANEAN" = 13
Now since E and R are fixed at the 1st and last place, so no. of letters left are 11.
We have to select 2 more letters to form a word with 4 letters.
We can have 2 cases:

Case 1: The letters can be the same ones

It can be seen that there are 2 E's, 2 N's and 2 A's in MDITERANEAN
So, the 2 letters can be selected in 3 ways.

Case 2: The letters are different

We can choose the 1st letter in 8 ways and the 2nd one in 7 ways.
Therefore, we can choose the two required letters in 8 * 7 = 56 ways

Therefore, required no. of ways = 3 + 56 = 59

The correct answer is A.
Anurag Mairal, Ph.D., MBA
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