Exam 10: Counting Methods

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. -Four representatives

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 19, 20, 21, 22, 23, 24, 25, 26, and 27 once. 22 20 23 25 19

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The white die shows a 3.

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The sum of the two dice is 8.

Solve the problem. -If 5 newborn babies are randomly selected, how many different gender sequences are possible?

Solve the problem. -Six strangers arrive at a business seminar and each person shakes hands with every other person. How many handshakes are there?

Solve the problem. -In how many ways can the number 44 be written as the sum of two primes?

Using the 36 possibilities found in the product table for rolling two dice, list and count the outcomes for which the sum (for both dice)is the following. -Less than 3

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. -A treasurer and a secretary if the two must not be the same sex

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 the four men occupy the four seats closest to the Aisle?

Evaluate the expression. - ${ } _ { 5 } C _ { 5 }$

Evaluate the factorial expression. - $\frac { n ! } { ( n - r ) ! }$ , where $n = 46$ and $r = 10$

Solve the problem. -A shoe store carries one brand of shoe in 4 different styles, 5 sizes, and 5 colors. How many different shoes are available of this one brand?

Solve the problem. -Which statement is true about row 3 in Pascal's Triangle?

Solve the problem. -Given a committee of 8 women and 11 men, count the number of different ways of choosing a president, a secretary, and a treasurer, if the president must be a woman and the secretary and Treasurer must be men. Assume no one can hold more than one office.

In a certain lottery, 5 different numbers between 1 and 9 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the Numbers are drawn is not important.

Find the number of ways to get the following card combinations from a 52-card deck. -All cards of the same color in a five-card hand

Complete the magic (addition)square. A magic square has the property that the sum of the numbers in any row, column, or diagonal is the same. -Use each number 14, 15, 16, 17, 18, 19, 20, 21, and 22 once. 19 18 16 15 22

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The red die shows a 3.

Solve the problem. -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.