factorials
warm up
double double
triple's alley
200

5!

120

200

Letty folds a piece of paper, then pokes holes into the paper and unfolds it again.
The unfolded paper looks like this:

b

200

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

200

In how many ways can I stack 5 books on a shelf?

120

200

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

.

300

2!

2

300

Barbie has 6 hats and 5 dresses. How many hat-and-dress outfits can she make?

30

300

In how many ways can I arrange four different books on a shelf?

24

300

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

300

(42!)/(40!)

1,722

400

4!+3!

30

400

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

400

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

400

(5!)/(4!)

5

400

6!-5!

600

500

5!-4!

96

500

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

500

(5!)/(3!)

20

500

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

500

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