Combinations Formative - Marissa Considine | Library

Determine whether each problem represents a combination _nC_r or permutation _nP_r, then solve.

1

A basketball team has 12 players. If 5 players start the game, how many “starting” groups can the coach select?

1

How many "starting” groups can the coach select if he assigns each player a position as well?

1

A relay race has 4 runners who run different parts of the race. There are 10 students on the team. In how many ways can the coach select the students to compete in the race?

1

You can order a hamburger with cheese, onion, pickle, relish, mustard, lettuce, tomato, or mayonnaise. How many different combinations of the “extras” can you order, when you choose 4 of them?

1

In how many ways can 8 people be lined up in a row for a photograph?

1

A person working quality control will select samples of their products and test them to make sure they work correctly. Out of 100 mousetraps that were produced, the inspector will choose a group of 4. How many different groups can be selected?

1

A club contains the President, the Secretary, and 8 other members. The club is asked to send a group of 4 representatives to a conference. Calculate the number of different ways in which the group can be formed.

1

Evaulate

1

Evaulate

1

Griffin got a girls phone number, but the piece of paper it was written on got chewed up by his dog. He found all of the numbers, but he doesn't know what order they go in. How many different numbers will he have to call before he gets the right number?

1

How many ways can you elect 4 candidates to a municipal planning board from a field of 7 candidates.

1

Six representatives from a senior class of 125 students are to be chosen for the student council. In how many ways can these students be chosen to represent the senior class on student council?

1

How many ways can you check out 3 library books from a list of 8 books for a research paper?

1

Mrs. Considine is holding a raffle for extra credit for anyone that finishes this assignment in class. If she chooses 2 winners from 15 students, how many different pairs of students can win?

Example
A group of 6 sophomores, 8 juniors, and 9 seniors apply to go on a community service trip.  The school will pick 2 sophomores, 2 juniors, and 4 seniors.  How many different groups can be selected?

Sophomores: _6C_2
Juniors: _8C_2
Seniors: _9C_4

_6C_2 \times _8C_2 \times _9C_4=15\times 28\times 126=52920 groups.

1

A group of 6 juniors and 6 seniors apply for a leadership committee. The school will pick 3 juniors and 3 seniors to form the commitee. How many different groups can be selected?

1

A week before summer starts, 22 children (age 6-12) and 30 teenagers (age 13-19) sign up for a basketball camp. The camp is almost at capacity and can only accept 5 children and 5 teenagers from this group. How many different groups can be selected?

1