Question 1 : We would like to test 3 different treatments on a particu-

Question

lar type of plant. A worker at the local greenhouse will allow us to use 3
among 10 plants. Note: Each treatment will be used on one and only one
plant.

a) In how many different ways can we assign the plants to the treatments?

b) Suppose that 2 of the ten plants are older than the other 8 plants. Assuming that we are choosing the plants randomly, what is the probability that at least one of the two older plants will be chosen among the three selected
plants?

There are 10C3 10 choose 3 ways to select a plant, and 3 solutions we could use on a plant. You should be able to calculate this.
The easier way to calculate b) is to observe that there are
8C3 ways to select only younger plants out of 10C3 total ways to select plants. Thus the prob of only younger plants is
(8C3)/(10C3) and the prob that at least on plant is an older one is
1 - (8C3)/(10C3)