the unique set of letters are:

ASINTO

the repeated set of letters:

SASSAIN (ie. 3 S's + 2 A's + 1 I + 1 N)

the answer is case 1 + case 2+ case 3 + case 4 + case 5

making a combination of 4 from the unique letters is 6C4

take 1 repeated S + the S from the unique set of letters + any other 2 unique letters. So, 5C2

do the same thing using A, N & I (ie. taking 1 repeated & the corresponding letter from the unique set of letters)

so, totally, 4*5C2

take the 2 repeated A's + the A from the unique set +1 other unique letter. so, 5C1

do the same for S's

so totally, 2*5C1

take the 3 repeated S's + the unique S. so 1 combination

(2 I's + 2 N's) + (2I's + 2S's) + (2I's + 2A's) + (2N's + 2A's) + (2N's + 2S's) + (2S's + 2A's) = 6

total (ANSWER) = 6C4 + 4*5C2 + 2*5C1 + 1 + 6

                            15 + 40 + 10 + 1 + 6 = 72

 

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