Might be easy
Jason owns 10 shirts, 5 pairs of pants, and 3 pairs of shoes. How many different outfits can Jason make?
10*5*3 = 150
Dr. Kitchens wishes to form a five-person committee to revise the teacher handbook. If she chooses five teachers at random from the 42 available teachers, how many different possible committees are there?
42 C 5 = 850,668
An instructor gives an exam with 14 questions. Students are allowed to choose any 10 questions to answer. How many different choices of 10 questions are there?
14 C 10 = 1001
In poker, the player is dealt 5 cards from a deck of 52. How many distinct poker hands are possible?
52 C 5 = 2,598,960
7! = 5040
How many four-digit numbers end with a 3?
9*10*10*1 = 900
A Little League baseball team has 12 players available for a 9-member team (no designated team positions). How many different 9-member teams and 2 alternates are possible?
12 C 9 * 3 C 2 = 220*3 = 660
Come up with a counting situation that would result in an answer of 8C3
Answers will vary.
A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. How many different ways can a doctor prescribe the drug for a patient suffering from asthma?
5*3*2 = 30
On the last day of the month, Ms. Kirby gives a free 100 quiz grade to three randomly selected students in each class who have had perfect attendance for the month. During the month of October, 17 students in statistics had perfect attendance. In how many ways can Ms. Kirby select the students?
17 C 3 = 680
A multiple-choice test consists of 10 questions with choices a, b, c, d, e. How many different ways are there to complete the test? (i.e. put an answer for every question)
510 = 9,765,625
Greg's new password must contain three upper case letters followed by two digits (0 - 9). How many possible passwords could Greg create if the first letter cannot be a vowel, and the digits can't repeat?
21*26*26*10*9 = 1,277,640
Greg's new password must contain three upper case letters followed by two digits (0 - 9). How many possible passwords could Greg create?
26*26*26*10*10 = 1,757,600
How many different 5-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6, 7?
7*7*7*7*7 = 16,807
Come up with a counting situation that would result in an answer of 8P3
Answers will vary
How many 5-card poker hands can be dealt with a four of a kind? A four of a kind poker hand is all four cards of one rank and then one other card.
13*48 = 624
A travelling salesman has time to visit 5 of the 16 stores on his list. How many different routes are possible?
16 P 5 = 524,160
A Little League baseball team has 12 players available for a 9-member team (no designated team positions). How many different 9-member teams are possible?
12 C 9 = 220
Count the number of license plates which either consist of three capital English letters, followed by three digits, or consist of two digits followed by four capital English letters.
26*26*26*10*10*10 + 10*10*26*26*26*26 = 63,273,600
A professor has seven books on discrete mathematics, five on number theory, and four on abstract algebra. In how many ways can a student borrow two books not both on the same subject?
7*5 + 7*4 + 5*4 = 83