# Worksheet: Using Combinations to Count Outcomes

Q1:

Determine the number of ways a team of 119 people can be chosen out of a group of 120.

Q2:

Determine the number of ways a team of 2 people can be chosen out of a group of 17.

Q3:

A class contains 27 boys and 29 girls. In how many ways can you select a team of 4 people from the class such that every member of the team is of the same sex?

Q4:

Determine the number of ways a committee of 7 people, consisting of 5 boys and 2 girls, can be formed from a group of 9 boys and 4 girls.

Q5:

Determine the number of ways to choose 3 people from 55.

Q6:

In how many diﬀerent ways can 71 people be picked from 74?

Q7:

In a science fair experiment, three units are selected for testing out of every 587 units produced. In how many ways can these three units be selected?

Q8:

How many 3-card hands can be chosen from a deck of 52 cards?

Q9:

Walter has enough money to purchase only two books from the six he wants to read. Determine the number of ways he can choose them.

Q10:

How many ways can a committee of 3 freshmen and 4 juniors be formed from a group of 8 freshmen and 11 juniors?

Q11:

Madison wants to visit cities across the US, and she has placed the names of 32 cities into a hat. If she randomly draws 3 names from the hat, what is the probability that she gets Savannah, Austin, and Seattle?

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Q12:

How many lines are determined by 112 randomly drawn points, where no three of which are collinear?

Q13:

How many lines are determined by 44 randomly drawn points, where no three of which are collinear?

Q14:

Andrea invited 4 of her 24 friends over for a movie night. If she chose to invite her friends at random, what is the probability that Cynthia, Judith, Molly, and Sandra are chosen?

• A0
• B
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• E