The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS…

Question

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:

Accepted Answer

$\begin{gathered} 2M \ 2A \ 2T \ H,E,I,C,S \end{gathered}$

Case-I

2 Alike 2 Alike 1 Diff

${}^{3}{C}_{2}	imes {}^{6}{C}_{1}=18$

Case-II

2 Alike + 3 Diff

${}^{3}{C}_{1}	imes {}^{7}{C}_{3}=105$

Case-III

All different

${}^{8}{C}_{5}=56$

Total ways $=179$

Solutions · 1