The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to [2024]
175
181
179
177
(3)
We have, MMAATTHEICS
Case-I : All distinct =C58=56
Case-II : 2 identical + 3 distinct =C1×C3=10573
Case-III : 2 identical + 2 identical + 1 distinct =C2×C16=183
Hence, total number of ways = 56 + 105 + 18 = 179
