Question

The number of ways in which the letters of the word $STRANGE$ can be arranged so that the vowels may appear in the odd places is

• A. $1370$
• B. $1440$
• C. $1470$
• D. None of these

Answer 1

The correct option is B $1440$

2 vowels, 5 consonants, 3 even and 4 odd places.

2 vowels (a,e) can be arranged in 4 odd places in ${{}^{4}C}_2=12$ ways and 5 consonants can be placed in 5 blank places in ${{}^{5}C}_5=5!=120$ ways

Hence, by fundamental theorem, total ways $=12\times 120=1440$