Math Problems: Stud. Congress - Coin Toss - Prod. Table - Combos

MGF 1106 Liberal Arts Mathematics

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Task

Short Answer. Answer the indicated question.

Given a group of students: G = {Allen, Brenda, Chad, Dorothy, Eric} or G = {A, B, C, D, E}, list and count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.

1) Three representatives, if two must be male and one must be female.

Use a tree diagram showing all possible results when four fair coins are tossed. Then list the ways of getting the indicated result.

2) at least two tails

Solve the problem.

3) Construct a product table showing all possible two-digit numbers using digits from the set {1, 2, 6, 7}. List the prime numbers in the table.

4) A saleswoman packed 3 jackets and 5 skirts. With one jacket, she could wear all 5 skirts. With another jacket, she could wear 4 skirts. With the third jacket, she could wear only 3 skirts. How many different combinations did she have?

5) License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?
6) How many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of digits is allowed.
7) Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if all the women sit together and all the men sit together?

8) Four married couples have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if there are no restrictions on the seating arrangement?

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