factorials
warm up
double double
triple's alley
place your bet
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
