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We have, 6 objects {A}, {S}, {S}, {I}, {S}, {T} and there are 3 S's.

The S’s can be arranged in following two ways to form a six letter word in which the S’s alternate with other letters, is as shown below:

S×S×S× and ×S×S×S where the ‘×’ are to be filled with the other letters.

Now, for the other 3 positions we have to place A, I and T, so, 3 positions can be filled with 3 letters in 3!

= 6 ways.

The number of six letter words that can be formed using the letters of the word “ASSIST” in which S’s alternate with other letters is

= 12.

The discussion can be shown pictorially as:

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