Question

The number of ways in which the letters of the word ${}^{\prime \prime }STRANG{E}^{\prime \prime }$ can be arranged so that the vowels may appear in the odd place, is

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

Answer 1

The correct option is A $1440$

There are $5$ consonants and $2$ vowels in the word $STRANGE$.

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

$=5\times 4\times 5\times 3\times 2\times 1=120$ ways.

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