Fundamental Counting Principle
Fundamentals of Probability
Combination
Permutation
100
A restaurant offers 8 appetizers and 11 main courses. In how many ways can a person order a two-course meal?
What is 88.
100
You are dealt one card from a standard 52-card deck. Find the probability of being dealt an 8.
What is 1/13.
100

A pizza shop offers 8 toppings. You want to choose exactly 3 different toppings for your pizza. How many possible topping combinations can you make?

What is 56?
100

A race has 6 runners. In how many different ways can the runners finish 1st, 2nd, and 3rd?


What is 120?

200

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.  How many combinations of main course, vegetables, beverages, and desserts? 

What is 144.

200
You are dealt one card from a standard 52-card deck. Find the probability of being dealt the ace of diamonds.
What is 1/52.
200

A student council must choose 4 representatives from a group of 10 students. How many different groups of representatives can be formed?

What is 210

200

A student creates a 4-digit lock code using the digits 1, 2, 3, 4, and 5 without repeating any digits. How many different lock codes are possible?

What is 120?

300
A person can order a new car with a choice of 15 possible colors, with or without air conditioning, with or without automatic transmission, with or without power windows, and with or without a CD player. In how many different ways can a new car be ordered with regard to these options?
What is 240.
300
You are dealt one card from a standard 52-card deck. Find the probability of being dealt a diamond and a spade.
What is 0.
300

A teacher wants to randomly select 5 books from a shelf containing 12 different books. In how many ways can the books be chosen?

What is 792?

300

Seven books are placed on a shelf. In how many different ways can the books be arranged if two particular books must be next to each other?

What is 1440? 

6! = 720.  
Arrange the pair internally: 2! = 2

720(2) = 1440

400
A stock can go up, go down, or stay unchanged. How many possibilities are there if you own 7 stocks?
What is 2187.
400
A fair coin is tossed 2 times in succession. The set of equally likely outcomes is {HH,HT,TH,TT}. Find the probability of getting a head on the second toss.
What is 1/2.
400

A basketball coach needs to choose 2 captains and 3 assistant captains from 9 players, but all 5 roles are simply selections (order does not matter). How many possible groups of 5 leaders can be selected?

What is 126?

400

How many distinct arrangements can be made using all the letters in the word MATH?


What is 24? 

(4! = 24) 

500
How many five-digit odd numbers are possible if the leftmost digit cannot be zero?
What is 45,000.
500

A weather forecast states that the probability of rain tomorrow is 1/2. Which answer below correctly interprets this statement?

(A) The statement does not make sense because probabilities cannot be split equally between outcomes.
(B) The statement means there is an equal chance that it will rain or that it will not rain.

What is B.

500

A committee of 6 people must be formed from 15 volunteers, but two particular volunteers refuse to serve together. How many valid committees can be created?

What is 4719?

15C6 = 5005 (total)  13C4 = 286 (containing both specific volunteers).  
Valid committees: 5005 - 286 = 4719

500

How many distinct arrangements can be made using all the letters in the word STATISTICS?

What is 50,400? 

S appears 3 times, T appears 3 times, I appears 2 times, A and C each appear once.
10! /(3!3!2!) = 50,400

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