Question

How many six letter words be made out of the letters of $ASSIST$ ? In how many words the alphabets $S$ alternates with other letters ?

• A. $120,6$
• B. $720,12$
• C. $120,12$
• D. $720,24$

Answer 1

The correct option is C $120,12$

The word ASSIST has 3 's' and 3 other characters (AIT).

Place the other 3 characters first. This can be done in 3! ways.

Now there are 4 spaces remaining (1234) mark as 1,2,3,4.

3 's' 5 can be placed at the spaces marked as 1,2,3 or at the spaces marked as 2,3,4 (2)was

Total no.of ways =3! .2$=3\times 2\times 2=12$

Total no.of ways =5!.$=5\times 4\times 3\times 2=120.$

$\therefore$ so, the answer is 120,12.