Question

Words are formed by arranging the letters of the word "STRANGE" in all possible manner. Let $m$ be the number of words in which vowels do not come together and ${}^{\prime }{n}^{\prime }$ be the number of words in which vowels come together. Then find the ratio of $m:n$. (where $m$ and $n$ are coprime natural number).

• A. $\frac{16}{15}$
• B. $\frac{16}{21}$
• C. $\frac{15}{16}$
• D. None of the above

Answer 1

Answer: (C)

$\frac{15}{16}$

Two vowels a and e in "STRANGE"

four odd places , so ${}^4{C}_2$ ways $=6$

$A,E$ to be arranged in $2!$ ways =$2\times 6\times 120=1440$

$5$ constants arranged in $5!=120$

Let m be the no: of words in which vowels

do not come together $=$ STRNG(AE) $=2\times 7!=10800$ ways

Let n be the no: of words in which vowels come together $=$ STRNG(AE) $=6!=720$ ways

$\therefore$ $\frac{m}{n}=\frac{10800}{720}=\frac{15}{16}$