Question

1. 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

Using combination we have

1) The number of ways is

2) The number of ways is

$\binom{102}{2}={102!\over (102-2)!2!}\\~~~~~ ~~~~~~~~={102\times 101\over 2\times 1}\\~~~~~ ~~~~~~~~=5151$