Introduction to Combinations

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Show your work for each problem.

1.
Which formula represents the number of combinations when choosing items from items?
1. a)
2. b)
3. c)
4. d)
2.
When should you use combinations instead of permutations?
1. a)When order does not matter
2. b)When items can repeat
3. c)When order matters
4. d)When selecting one item
3.
Calculate .
4.
Calculate .
5.
A bag has 6 different colored marbles. In how many ways can you choose 2 marbles?
6.
Why is ?
1. a)Both equal 21 by coincidence
2. b)The formula has two solutions
3. c)It's a calculation error
4. d)Choosing 3 to include is the same as choosing 4 to exclude
7.
Calculate .
8.
A class has 10 students. How many ways can the teacher choose 3 students for a group project?
9.
A restaurant offers 9 appetizers. How many ways can a customer choose 4 different appetizers?
10.
A bookshelf has 8 different books. In how many ways can you select 5 books to take on vacation?
11.
A standard deck has 52 cards. Which expression gives the number of 5-card hands?
1. a)
2. b)
3. c)
4. d)
12.
Calculate .
13.
A committee of 5 must be chosen from 8 men and 6 women. How many committees have exactly 3 men and 2 women?
14.
In a lottery, you choose 6 numbers from 1 to 45. How many different tickets are possible?
15.
If , what is ?
1. a)
2. b)
3. c)
4. d)
16.
A student must answer 8 questions out of 12 on an exam. In how many ways can this be done if the first 2 questions are mandatory?