MHT CET · Maths · Permutation Combination
The number of ways in which the letters of the word MACHINE can be arranged such that the vowels may occupy only odd positions, is
- A 288
- B 625
- C 576
- D 1152
Answer & Solution
Correct Answer
(C) 576
Step-by-step Solution
Detailed explanation
A, I, E (3 vowels)
M, C, H, N (4 consonants)
There are 4 odd places. So, three vowels can be arranged in four places in \(4_{\mathrm{P}_3}\) ways and 4 consonants can be arranged in remaining four places in \(4_{\mathrm{P}_4}\) ways.
Hence total number of ways \(=4_{\mathrm{P}_3} \times 4_{\mathrm{P}_4}=576\)
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