Question

a) How many different words can be formed using the letters of the word HARYANA?
b) How many of these begin with H and end with N?
c) In how many of these H and N are together?

Answer 1

HARAYANA

$\left(1\right)$ No. of words that can be formed$=\frac{7!}{3!}=\frac{7\times 6\times 5\times 4\times 3!}{3!}=840$ words

$\left(2\right)$ H_____N

No. of such words$=\frac{5!}{3!}=\frac{5\times 4\times 3!}{3!}=20$ words

$\left(3\right)$ $H$ and$N$ together be taken as one letter and can be arranged among themselves in $2!$ also $A$ is repeated $3$ times.

No. of such wordss$=\frac{2!\times 6!}{3!}=\frac{2\times 6\times 5\times 4\times 3!}{3!}=240$ words