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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? |
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Answer» The first letter is E and the last one is R. THEREFORE, one has to find two more letters from the remaining 11 letters. Of the 11 letters, there are 2 Ns, 2Es and 2AS and one each of the remaining 5 letters. The second and third positions can either have two different letters or have both the letters to be the same. Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways. Case 2: When the two letters are same. There are 3 OPTIONS - the three can be either Ns or Es or As. Therefore, 3 ways. Total NUMBER of possibilities = 56 + 3 = 59. The first letter is E and the last one is R. Therefore, one has to find two more letters from the remaining 11 letters. Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters. The second and third positions can either have two different letters or have both the letters to be the same. Case 1: When the two letters are different. One has to choose two different letters from the 8 available different choices. This can be done in 8 * 7 = 56 ways. Case 2: When the two letters are same. There are 3 options - the three can be either Ns or Es or As. Therefore, 3 ways. Total number of possibilities = 56 + 3 = 59. |
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