a. How many distinguishable arrangements are there using the
letters from the word STATISTICS?STATISTICS is a 10-letter word. If we could tell the S's apart,
the I's apart, and the T's apart, the answer would be 10! But
since we cannot, we must divide the 10! by the product of the
factorials of the number of S's, I's, and T's, or 3!*2!*3!
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b. Let’s define a substring to be an arrangement with a specific
condition. Consider the substrings that contain the 3 T’s in a
row … for example SAISICSTTT, or TTTSASSICI would be two such
substrings. How many of the arrangements in part (a) contain
none of these substrings?First we calculate the number of distinguishable substrings, then
subtract what we get from 50400.
The distinguishable substrings are the distinguishable arrangements
of ACIISSS(TTT), where the (TTT) is considered as a single character.
That's 8 characters, where the two I's and the the three S's are
indistinguishable, so the number of distinguishable substrings is
So we subtract 50400-3360 = 47040
Edwin
