how many five letter words can be formed using letters of word MANAGEMENT such that the two alike letters are there then they are always together
You can look at the Wikipedia page on the "Multinomial theorem". In the section "Number of unique permutations of words" it shows you the answer
Letters with multiplicities are (M2, A2, N2, G1, E2, T1).
How five letter words with 1M 1A 1N 1G 1E?
How five letter words with 2M's 1A 1N 1G?
How five letter words with 2M's 2A's and 1N?
After knowing this, what is one way to count all the possibilities?