5!
120
Letty folds a piece of paper, then pokes holes into the paper and unfolds it again.
The unfolded paper looks like this:
b
In how many ways can we form an international commission if we must choose one European country from among 6 European countries, one Asian country from among 4, one North American country from among 3, and one African country from among 7?
504 possibilities
In how many ways can I stack 5 books on a shelf?
120
Suppose that I have 6 different books, 2 of which are math books. In how many ways can I stack my 6 books on a shelf if I want a math book on both ends of the stack?
48
.
2!
2
Barbie has 6 hats and 5 dresses. How many hat-and-dress outfits can she make?
30
In how many ways can I arrange four different books on a shelf?
24
Your math club has 20 members. In how many ways can it select a president, a vice-president, and a treasurer if no member can hold more than one office?
6840 ways
(42!)/(40!)
1,722
4!+3!
30
You have three shirts and four pairs of pants. How many outfits consisting of one shirt and one pair of pants can you make?
12 outfits
For each of 8 colors, Barbie has one hat and one dress of that color. How many hat-and-dress outfits can she make if she refuses to wear a hat and a dress of the same color?
56
(5!)/(4!)
5
6!-5!
600
5!-4!
96
There are 8 sprinters in the Olympic 100-meter finals. The gold medal goes to first place, silver to second, and bronze to third. In how many ways can the medals be awarded?
336
(5!)/(3!)
20
In how many ways can we form a license plate if there are 7 characters, none of which is the letter O, the first of which is a numerical digit (0-9), the second of which is a letter, and the remaining five of which can be either a digit or a letter (but not the letter O)?
(calculator allowed)
13,130,468,750
My club has 15 members. In how many ways can we choose a president, vice-president, secretary, and treasurer, if no member can hold more than one office?
32,760