MHT CET · Maths · Permutation Combination
All letters of the word 'CEASE' are arranged randomly in a row, then the probability that two \(\mathrm{E}\) are found together is
- A \(\frac{7}{5}\)
- B \(\frac{3}{5}\)
- C \(\frac{2}{5}\)
- D \(\frac{1}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{5}\)
Step-by-step Solution
Detailed explanation
Sample space arrangement for the word 'CEASE' \(=5\) !
Here, \(\mathrm{E} \rightarrow 2, \mathrm{C} \rightarrow 1, \mathrm{~A} \rightarrow 1, \mathrm{~S} \rightarrow 1\)
Now, consider \(2 \mathrm{E}\) as one character, so that arranging for four letters \(=4 !\) ways
\(\therefore\) Required probability \(=\frac{4 !}{5 !}=\frac{1}{5}\)
Here, \(\mathrm{E} \rightarrow 2, \mathrm{C} \rightarrow 1, \mathrm{~A} \rightarrow 1, \mathrm{~S} \rightarrow 1\)
Now, consider \(2 \mathrm{E}\) as one character, so that arranging for four letters \(=4 !\) ways
\(\therefore\) Required probability \(=\frac{4 !}{5 !}=\frac{1}{5}\)
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