Fundamental Counting Principle
Factorials
Permutations
100
In how many different ways can you flip 4 fair-sided coins?
16 or 2 x 2 x 2 x 2
100
Evaluate 2!
= 1 x 2 OR 2
100

Suppose the first, second, and third place winners are supposed to be selected from 17 contestants. Without a calculator, write an expression to show how many ways these spots can be chosen?

17 P 3 OR 17!/14! OR 17 x 16 x 15

200
A movie theater sells 3 sizes of popcorn (small, medium, and large) with 3 choices of toppings (no butter, butter, extra butter). How many possible ways can a bag of popcorn be purchased?
9 or 3 x 3
200
Evaluate 0!
1
200

Without a calculator, write an expression for 13 P 4

13!/9! OR 13 x 12 x 11 x 10

300

A certain state issues license plates where 4 letters are followed by 2 single-digit numbers. How many different plates can be created if letters can be repeated but digits cannot? Do not solve, only use the counting principle.

26 x 26 x 26 x 26 x 10 x 9

300
Simplify 10!/8!
10 x 9 OR 90
300

In how many ways the letters of the word STRESS can be arranged ?

120

400
Using the digits 0, 1, 2, 3 and 5, how many ODD, 4-digit numbers that are greater than 3000 can be formed?
2 x 5 x 5 x 3 OR 150
400
Which is larger? 50!/(47!3!) or 100!/99!
50!/ (47!3!) = (50 x 49 x 48)/(3 x 2 x 1) = 50 x 49 x 16 100!/99! = 100 The first is larger
400
In how many ways can you arrange the letters in the word "COMBINATION"?
11!/(2!2!2!)
500
A 5-sided die, a 3-sided die, and a 7 sided-die are rolled simultaneously. How many elements are there in the sample space for this event?
105 or 5 x 3 x 7
500
What is n!/(n-1)! ?
n
500
Write a word for which there are 60 unique permutations of the letters.
The word should have 5 letters with one repeated letter
M
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n
u