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?
We have to arrange the cars for first 5 positions. This is a problem of permutations and is equivalent to form arrangements of 5 objects from 43 objects.
Thus, there are 115511760 ways to place the 43 cars in top 5.
Question 2)
Total number of students = 102 Number of students that should be together = 2
Making pairs from a group of students is equivalent to making combinations. So this is a problem of combinations and is equivalent to forming combination of 2 objects from 102.
So, the number of pairs that can be formed = 102C2 [tex]= \frac{102!}{2!*100!} \\ \\
=5151[/tex]
This mean with 102 students 5151 pairs of students are possible.
