How many 5 letter words can be formed from the word MANAGEMENT if two alike letters are always together?
My approach was like this:
The letters M, N, A , E appear twice and G, T appear once.
So, the first case was where all the letters were different, thus, the number of words formed were:
6C5 . 5!(further permutation) = 720
the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:
2C1 . 4C2 . 3! = 72
the third case was where there were one group of two alike letters and three different letters.
Thus, the number of words formed were:
4C1 . 5C3 . 4!= 960
thus, the total number of words were:
720 + 72 + 960 = 1752
but this answer is wrong as the Real answer is 1824.
Where was I wrong? Please explain.