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3. How many distinguishable permutations of the word ELLIPSES are there? Solution: n=8 In the word ELLIPSES there are 2 E's. 2 L's and 2 S' Using the formula: P=frac n!p!q!r!..frac 8!2!2!2!=frac 8 . 7 . 6 . 5 . 4 . 3 . 2 . 12 . 1 . 2 . 1 . 2 . 1=frac 8 . 7 . 6 . 5 . 4 . 3 . 2 . 18=5040 There are 5,040 distinguishable permutations from the word ELLIPSES 4. In how many ways can 7 children be seated in a round table? Use circular permutation where n=7 P=n-1!=7-1!=6!=6.5 . 4 . 3 . 2=120 way s. 5. In how many ways can a family of 6 members be seated in a circular table if two of them insist sitting beside each other? If two of them insist to sit beside each other, count them as one.
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