Exam 10: Counting Methods

Solve the problem. -Find the number of different three-member committees that could be selected from the group of {Mary, Norman, Paula, Raymond, Sally} given that Sally must be on the committee.

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

If two fair dice, one red and one white, are rolled, in how many ways can the result be obtained? -The product of the numbers on the two dice is a perfect square.

Use a tree diagram showing all possible results when a die is rolled twice. List the ways of getting the following result. -The sum of the numbers showing is 8.

Solve the problem. -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.

Solve the problem. -How many different 4-letter radio-station call letters can be made if the first letter must be K or W, repeats are allowed, but the call letters cannot end in an O?

Solve the problem. -If you toss six fair coins, in how many ways can you obtain at least two heads?

Solve the problem. -Given a group of students: $\mathrm { G } = \{$ Allen, Brenda, Chad, Dorothy, Eric $\}$ , count the number of different ways of choosing a treasurer and a secretary if the two must not be the same sex.

Solve the problem. -Which statement is true about row 2 in Pascal's Triangle?

Read each combination value directly from Pascal's Triangle. - ${ } _ { 5 } \mathrm { C } _ { 1 }$

Evaluate the factorial expression. - $\frac { 4 ! } { 6 ! }$

Evaluate the factorial expression. - $\frac { 6 ! } { 4 ! }$

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. -Multiple of 11

Provide an appropriate response. -Consider the selection of a thirteen card bridge hand. Is this a combination, a permutation, or neither?

Use a tree diagram showing all possible results when a die is rolled twice. List the ways of getting the following result. -The sum of the numbers showing is either 4 or 5 and one die is a 2.

Provide an appropriate response. -Consider the following counting problem. Eight women and seven men are waiting in line at a movie theater. How many ways are there to arrange these 15 people amongst themselves such that The eight women occupy the first eight places and the seven men the last seven places? To solve this problem, which of the following rules would you use?

Find the number of ways to get the following card combinations from a 52-card deck. -Two red kings and two black jacks

Solve the problem. -There are 5 women running in a race. How many different ways could first, second, and third place finishers occur?

Solve the problem. -A group of five entertainers will be selected from a group of twenty entertainers that includes Small and Trout. In how many ways could the group of five include at least one of the entertainers Small and Trout?

A student is told to work any 6 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.)