Three friends agreed to meet at 8 P.M. in on of the Spanish restaurants in town. Unfortunately they

Yahir Crane

Yahir Crane

Answered question

2022-06-15

Three friends agreed to meet at 8 P.M. in on of the Spanish restaurants in town. Unfortunately they forgot to specify the name of the restaurant. If there are 10 Spanish restaurants
(a) find the number of ways they could miss each other
(b) find the number of ways they could meet
(c) find the number of ways at least two of them meet each other.

I got 10 * 3 = 30 ways for (a) for (b), I got 10 ways. how do I do (c)?

Answer & Explanation

Cristian Hamilton

Cristian Hamilton

Beginner2022-06-16Added 23 answers

I’m afraid that you’ll have to start by redoing (a) and (b): both are wrong. Call the friends A, B, and C.

(a) I’m assuming that what’s wanted here is the number of ways in which they completely miss one another: no two go to the same restaurant. There are 10 restaurants that A could choose. B could then choose any of the remaining 9, and C could choose any of the 8 not chosen by A or B. Thus, there are 10 9 8 = 720 different ways in which they could completely miss one another.

(b) In order for them to meet successfully, they must all choose the same restaurant. There are 10 restaurants, so there are just 10 ways in which they can meet successfully. Alternatively, we can apply the same kind of analysis as in (a): A has a choice of 10 restaurants, but after that B and C have only 1 choice each, if the meeting is to take place, so the total number of ways is 10 1 1 = 10.

(c) This is most easily done by considering the complementary (opposite) event: no two of them meet. In (a) we calculated the number of ways in which this can happen. If there are n different ways in which could they choose restaurants, regardless of how many of them meet, the number of ways in which at least two of them meet must be n 720. What’s n?
Llubanipo

Llubanipo

Beginner2022-06-17Added 9 answers

n = 1000
So, so the answer to (c) is 1000 720 = 280.

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