MHT CET · Maths · Permutation Combination
The number of arrangements, of the letters of the word MANAMA in which two M's do not appear adjacent, is
- A 40
- B 60
- C 80
- D 100
Answer & Solution
Correct Answer
(A) 40
Step-by-step Solution
Detailed explanation
There are 6 letters.
M repeats 2 times,
A repeats 3 times.
We first arrange all letters except \(2 \mathrm{M}^{\prime} \mathrm{s}\) in \(\frac{4!}{3!}\) \(=4\) ways
These 4 letters create 5 gaps, where we can arrange \(2 \mathrm{M}^{\prime} \mathrm{s}\) in \(\frac{{ }^5 \mathrm{p}_2}{2!}=10\) ways
\(\therefore\) Required number of arrangements \(=4 \times 10=40\)
M repeats 2 times,
A repeats 3 times.
We first arrange all letters except \(2 \mathrm{M}^{\prime} \mathrm{s}\) in \(\frac{4!}{3!}\) \(=4\) ways
These 4 letters create 5 gaps, where we can arrange \(2 \mathrm{M}^{\prime} \mathrm{s}\) in \(\frac{{ }^5 \mathrm{p}_2}{2!}=10\) ways
\(\therefore\) Required number of arrangements \(=4 \times 10=40\)
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