Fundamental Counting Principle
A restaurant offers 8 appetizers and 11 main courses. In how many ways can a person order a two-course meal?
What is 88.
There are 9 performers who will present their comedy acts this weekend at a comedy club. One of the performers insists on being the last stand-up comic act of the evening. If this performer's request is granted, how many different ways are there to schedule the appearances?
What is 40,320.
8!
An election ballot asks voters to select five city commissioners from a group of eighteen candidates. In how many ways can this be done?
What is 8,568.
18!/(5!13!)
Ian, Sarah, Maria, Simone, and Kim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time. Find the probability that Ian will arrive first and Kim last.
What is 1/20.
1/5 * 1/4
A restaurant offers the following limited lunch menu. Main Courses: Beef, Pork Roast, Duck, Quiche
Vegetables: Peas, Squash, Cauliflower, Eggplant
Beverages: Coffee, Tea, Milk
Desserts: Cake, Pie, Sherbert
What is 144.
(4)(4)(3)(3)
A club with 19 members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is to be held by one person and no person can hold more than one office, in how many ways can those offices be filled?
What is 5814.
19!/16!
A health inspector must visit 4 of 12 restaurants on Monday. In how many ways can she pick the 4 restaurants?
What is 495.
12!/(4!8!)
Six stand-up comics, A, B, C, D, E, and F, are to perform on single evening at a comedy club. The order of performance is determined by random selection. Find the probability that Comic D will perform last and Comic F will perform first.
What is 1/30.
1/6 * 1/5
A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 7 stocks?
What is 2187.
37
At a benefit concert, thirteen bands have volunteered but there is only enough time for six of the bands to play. How many lineups are possible?
What is 1,235,520.
13!/7!
How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, G, and H if no repetition of letters is allowed?
What is 1680.
8!/4!
A hand consists of 5 cards from a well-shuffled deck of 52 cards. A club flush is a 5-card hand consisting of all club cards. Find the probability of being a dealt a club flush. (Round to six decimals places as needed.)
What is 0.000495.
(13/52)(12/51)(11/50)(10/49)(9/48)
How many five-digit odd numbers are possible if the leftmost digit cannot be zero?
What is 45,000.
(9)(10)(10)(10)(5)
In how many distinct ways can the letters of the word ROBBER be arranged?
What is 180.
6!/(2!2!)
Using 9 flavors of ice cream, how many cones with 3 different flavors can you create if it is important to you which flavor goes on the top, middle, and bottom?
What is 504.
9!/6!
A fair coin is tossed 2 times in succession. Find the probability of getting a head on the second toss.
What is 1/2.
The digits 1,2,3,4, and 5 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 500.
What is 1/10.
(1/5)(1/2)