Class 11

Math

Algebra

Permutations and Combinations

The number of ways in which the letters of the word $_{′′}STRANGE_{′′}$ can be arranged so that the vowels may appear in the odd place, is

- $1440$
- $1470$
- $1370$
- None of these

Out of $7$ places for the $7$ letters, $4$ places are odd and $3$ places are even.

$2$ vowels can be arranged in $4$ odd places in $P(4,2)$ ways $=12$ ways and then $5$ consonants can be arranged in the remaining $5$ places in $P(5,5)$ ways

$=5×4×5×3×2×1=120$ ways.

Hence the required number of ways $=P(4,2)×P(5,5)=12×120=1440$.