Question

In how many ways can the letters of the word STRANGE be arranged so that the vowels may appear in the odd places?

• A. 720
• B. 1092
• C. 1440
• D. none of these

Answer 1

Answer: (C)

1440

There are 5 consonants and 2 vowels in the word STRANGE out of 7 places for the 7 letters, 4 places are odd and places are even.
2 vowels can be arranged in 4 odd places in ${=}^4{P}_2$ ways and then 5 consonants can be arranged in remaining 5 places in ${}^5{P}_5$ ways.
Hence, the required number of ways${=}^4{P}_2{\times }^5{P}_5=1440$