Problem #2, 6 and 7 are very basic problems.
If you can't do those, no wonder you're having difficulty.
I'm certain that these 8 problems is your entire assignment.
I can't imagine any problem that you could solve.
2. From 9 names on a ballot, a committee of 5 will be elected to attend a political national convention.
How many committees are possible?
This is a Combinations problem.
Choosing 5 objects from 9, there are: . ways.
5. A teacher and 12 students are to be seated along a bench in the bleachers.
In how many ways can this be done if the teacher must be seated in the middle
and the one difficult student in the class must sit to the teachers immediate left?
There are 13 people to arrange in a row.
Duct-tape the teacher and the difficult student together: .
Now we have 12 "people" to arrange:
. . [TS] and the 11 other students.
Consider the 12 positions: ._ _ _ _ _ _ _ _ _ _ _ _
Since the teacher must be "in the middle",
. . [TS] cannot occupy the first seat; it has 11 choices of seats.
Then the other 11 students can be seated in ways.
Therefore, there are: ways.
8.You are dealt 6 cards from a shuffled deck of 52.
Find the probability of getting 3 Jacks and 3 Aces.
There are: . possible outcomes.
We want 3 of the 4 available Jacks: . ways.
We want 3 of the 4 available Aces: . ways.
Hence, there are:. ways to get 3 Jacks and 3 Aces.