Question

In the word HARYANA, how many words can be formed with letters H and N are together?

Answer 1

Considering H and N together we have $7-2+1=6$ letters out of which three are alike i.e, A's and others are each of its own kind. These six letters can be arranged in $\frac{6!}{3!}$ ways. But Hand' N can be arranged amongst themselves in $2!$ ways.
Hence, the required number of words $=\frac{6!}{3!}\times 2!$
$=120\times 2=240.$