Question

There are 43 cars that start in every Nascar Sprint Cup race. How many ways can they place in the top 5 at each race?

2. There are 102 students in John's freshman seminar class at SUNY Oneonta. The professor tells her students she will be assigning a project in which the students will work in pairs and that she will be selecting the pairs of students. How many pairs of students are possible?

Answer 1

1. Assuming we're not concerned with the order of finish, the number is the number of ways 5 can be chosen from 43.

... C(43, 5) = 43!/(5!·(43-5)!) = (43·42·41·40·39)/(5·4·3·2·1) = 962,598

2. There are 102 choose 2 = C(102, 2) = 102*101/(2*1) = 5,151 ways to pair one student with another.

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There are more than 2.75×10⁸⁰ ways the class of 102 can be divided into pairs of students. That number is 102!/(51!·2⁵¹).