SOLUTION: 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?

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?

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?
thanks alot
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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?
----
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
---
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!
---
# of arrangements with the two sitting side-by-side = 14
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Ans: 8!- 14 = 40,305
======================
Cheers,
Stan H.

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a.
4!=group of four
5!=four individuals and the group
4!*5!=2880
.
b.
The two can sit together in only 14 ways
8!-14*6!
=40320-10080
=30240
.
Ed
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