Hi Ravi,

You have the arrangement

and you are to fill the empty places with the letters STRNG, in any order.

Start by placing one of the letters in the leftmost position. There are 5 choices for the letter you select. REgardless of the letter you choose there are 4 letters remaining and hence you have 4 choices for the letter to place beside the first letter you chose. Thus there are $5 \times 4$ choices for the first two letters. Again, regardless of which two letters you have already used there are 3 letters remaining and hence to fill the first 3 positions you have $5 \times 4 \times 3$ choices. Repeat this procedure for the remaining two positions to arrive at the total number of choices.

If you are also allowed to have the arrangement

then you will need to double the total number of possible arrangements.

Penny