JEE Mains · Maths · STD 11 - 6. permutation and combination
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 :
- A \(175\)
- B \(181\)
- C \(177\)
- D \(179\)
Answer & Solution
Correct Answer
(D) \(179\)
Step-by-step Solution
Detailed explanation
\(AA\), \(MM\), \(TT\), \(H\), \(I\), \(C\), \(S\), \(E\) (\(1\)) All distinct \({ }^8 \mathrm{C}_5 \rightarrow 56\) (\(2\)) \(2\) same, \(3\) different \({ }^3 \mathrm{C}_1 \times{ }^7 \mathrm{C}_3 \rightarrow 105\) (\(3\)) 2 same \(I^{\text {st }}\) kind, 2 same…
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