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HW 8.3 Permutations and Combinations

Last updated over 3 years ago

15 questions

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Question 1

1.

Solve.

Question 2

2.

Solve.

Question 3

3.

A high school is planning to put on the musical West Side Story. There are 20 singers auditioning for the musical. The director is looking for two singers who could sing a good duet. In how many ways can the director choose two singers from the 20 singers? Indicate if this is a permutation or a combination.

Combination

Permutation

Question 4

4.

The director is also interested in the number of ways to choose a lead singer and a backup singer. In how many ways can the director choose a lead singer and the a backup singer? Indicate if this is a permutation or a combination.

Combination

Permutation

Question 5

5.

How many groups of five songs can be chosen from a list of 35 songs?

Question 6

6.

How many ways can a person choose three different desserts from a dessert tray of eight desserts?

Question 7

7.

How many ways can a manager of a baseball team choose the lead-off batter and a second batter from a baseball team of nine players?

Question 8

8.

How many ways are there to place seven distinct pieces of art in a row?

Question 9

9.

How many ways are there to randomly select four balls without replacement from a container of 15 balls numbered 1 to 15?

Question 10

10.

A high school is planning to put on the musical West Side Story. There are 20 singers auditioning for the musical. The director is looking for two singers who could sing a good duet. What is the probability that Alicia and Juan are the two singers who are selected by the director?

Question 11

11.

The director is also interested in the number of ways to choose a lead singer and a backup singer. What is the probability that Alicia is selected the lead singer and Juan is selected the backup singer?

Question 12

12.

A bag contains 9 tiles, each with a different number 1 to 9. You choose a tile without looking, put it aside, choose a second tile without looking, put it side, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?

Question 13

13.

There are 11 students on a committee. To decide which 3 of these students will attend a conference, 3 names are chosen at random by pulling names one at a time from a hat. What is the probability that Sarah, Jamaal, and Mai are chosen in any order?

Question 14

14.

A school has 5 Spanish teachers and 4 French teachers. The school’s principal randomly chooses 2 of the teachers to attend a conference. What is the probability that the principal chooses 2 Spanish teachers?

Question 15

15.

There are 6 fiction books and 8 nonfiction books on a reading list. Your teacher randomly assigns you 4 books to read over the summer. What is the probability that you are assigned all nonfiction books?