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timurjin [86]
3 years ago
6

The Environmental Protection Agency must visit nine factories for complaints of air pollution. In how many ways can a representa

tive visit five of these to investigate this week? Since the representative's travel to visit the factories includes air travel, rental cars, etc., then the order of the visits will make a difference to the travel costs.
Mathematics
1 answer:
kirill115 [55]3 years ago
8 0

Answer:

The number of ways is  \left 9}\atop } \right. P _5 = 15120

Step-by-step explanation:

From the question we are told that

   The number of factories visited is  n = 9

    The number of factories to be visited by a representative  r = 5

The number of way to visit the 5 factories is mathematically represented as

         \left 9}\atop } \right. P _5 = \frac{9!}{(9-5)!}

Where P represents  permutation

  =>   \left 9}\atop } \right. P _5 = \frac{9 \ !}{4\ !}

 =>     \left 9}\atop } \right. P _5 = \frac{9 *8*7 * 6 * 5 * 4!}{4\ !}

=>    \left 9}\atop } \right. P _5 = 15120

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