Question 1)Total Number of Cars = 43
Number of positions = 5
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.
So, the number of ways to place the top 5= 43P5
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
This mean with 102 students 5151 pairs of students are possible.