One student burned a piece of paper weighing 4.8 grams. The table below shows the mass of the materials formed by burning the paper. Material formed
Mass of material (in grams)
Ash
2
Smoke
2.2
Dust
2.5
What is most likely the mass of the ash formed on burning the piece of paper?
0.1 grams
0.3 grams
4.6 grams
4.7 grams

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.