Consider a engineer who must visit nine manufacturing facili

Consider a engineer who must visit nine manufacturing facilities in a single day. (a) If each facility is distinct, how many visitation sequences are possible? (b) Reconsider part (a) if six facilities are production facilities and three facilities are packaging facilities, with facilities of the same type being indistinguishable. (c) Reconsider part (a) if five facilities are production facilities and four are packaging facilities. All facilities are distinguishable. The engineer begins the day by visiting a production facility, and alternates between types of facilities for the rest of the day (i.e., the second is a packaging facility, the third is a production facility, and so forth).

Solution

a)

There are

9! = 362880 ways [answer]

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b)

By permutation of like objects, there are

9!/(6!3!) = 84 [answer]

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c)

We can permute the production facilities, 5! = 120 ways.

We can also permut the packaging facilities, 4! = 24 ways.

Thus, there are 120*24 = 2880 ways [answer]