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

Question

Aicharya · Accepted Answer

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 $=4_{\mathrm{P}_3} 	imes 4_{\mathrm{P}_4}=576$

The number of ways in which the letters of the word MACHINE can be arranged such that the vowels may occupy…

Solution