Exam 10: Counting Methods

Solve the problem. -Find the number of different subsets of the set {0}.

A poker hand consists of 5 cards dealt from an ordinary deck of 52 playing cards. How many different hands are there consisting of four cards of one suit and one card of another suit?

Solve the problem. -Four accounting majors, two economics majors, and three marketing majors have interviewed for five different positions with a large company. Find the number of different ways that five of these People could be hired if the first position is to be filled by an accounting major, the second position Is to be filled by an economics major, the third position is to be filled by a marketing major, and The last two positions can be filled by any major.

Solve the problem. -A local department store sells carpets in 4 sizes. Each carpet comes in 3 different qualities. One of the sizes comes in 5 colors. The other sizes come in 3 colors. How many choices of carpet are there?

Evaluate the permutation. - ${ } _ { 9 } \mathrm { P } _ { 0 }$

Find the number of ways to get the following card combinations from a 52-card deck. -If three cards are successively dealt from a 52-card deck without replacement, in how many ways could they be a face card, then a spade, and then a heart?

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 male and one must be female

Solve the problem. -License plates are made using 2 letters followed by 2 digits. How many plates can be made if repetition of letters and digits is allowed?

Determine the number of figures (of any size)in the design. -Squares (of any size)

How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 8 members? Assume that no member can hold more than one office.

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 there must be two women and one man on the Committee.

Solve the problem. -How many 5-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?

A committee is to be chosen from a group of fourteen women and twelve men. Determine the number of ways of choosing a female president, a male treasurer, and three other members of Either gender. Assume that no one can hold more than one office.