Question 370342
a. Suppose we have a group of 8 students sitting on a long bench.
Four of the eight insist on sitting side-by-side. In how many ways can the eight students be seated on the bench?
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Treat the four as a block that can be arranged 4! ways
Treat the other four plus the block as 5 persons that
can be arranged in 5! ways
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Total arrangements = 4!*5! = 2880 arrangements
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b. Two of the eight insisting on not sitting side by side. In how many ways can the eight students be seated on the bench?
# of unrestricted arrangements = 8!
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# of arrangements with the two sitting side-by-side = 14
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Ans: 8!- 14 = 40,305
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Cheers,
Stan H.