Question

The answer to one and two

Answer 1

(a) There are 9 students entering the school district science project:

medals for 1st, 2nd and 3rd

k1 = 1O ways to choose first person to be chosen from the group of 10.

99

k2 = 8 ways for the second person to be chosen from the remaining people(9–1).

k3 = 7 ways for the second person to be chosen from the remaining people(8–1).

then all you need to do is multiply these k1 * k2 * k3.

`\begin{gathered} 1st\text{ 2nd 3rd} \\ 1st=9\text{ option} \\ 2nd=8\text{ }options \\ 3rd=7\text{ options} \end{gathered}`
`\begin{gathered} 9*8*7 \\ =504 \end{gathered}`

(b) There are 7 unique names in a bowl. In how many orders can 2 names be chosen:

This is a permutation problem in order

There are 7 names, and the 2 name have to be in same order

`\begin{gathered} 7P_2 \\ (7!)/((7-2)!) \\ =(7!)/(5!) \\ =(7*6*5!)/(5!) \\ =42 \end{gathered}`