Practice (page 7 of Unit 8 Lesson 4) - Write your answers to the practice below.
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1. Determine whether the given situation represents a permutation or a combination:
a) Choosing a president, a vice president, and a treasurer from a group of 10 candidates.
- This represents a permutation because the order in which the candidates are chosen for each position matters.
b) Selecting 3 books to read out of a set of 8 books.
- This represents a combination because the order in which the books are chosen does not matter.
2. Solve the following problems:
a) How many different arrangements can be made from the letters of the word "APPLE"?
- The word "APPLE" has 5 letters, so there are 5 options for the first letter, 4 options for the second letter, 3 options for the third letter, 2 options for the fourth letter, and 1 option for the fifth letter. Therefore, there are 5 x 4 x 3 x 2 x 1 = 120 different arrangements that can be made from the letters of the word "APPLE".
b) In how many ways can a teacher distribute 4 different books to 3 different students?
- Each book has 3 options for which student it can be given to. Therefore, there are 3 x 3 x 3 x 3 = 81 ways in which a teacher can distribute 4 different books to 3 different students.
c) A committee of 3 members is to be selected from a group of 8 people. How many different committees can be formed?
- This represents a combination because the order in which the members are chosen does not matter. Using the combination formula 8C3, there are (8!)/(3!(8-3)!) = 8 x 7 x 6/(3 x 2 x 1) = 56 different committees that can be formed.
d) Out of a group of 5 boys and 3 girls, how many different pairs can be chosen with 1 boy and 1 girl?
- There are 5 options for choosing a boy and 3 options for choosing a girl. Therefore, there are 5 x 3 = 15 different pairs that can be chosen with 1 boy and 1 girl from the group.