Permutations
Twelve cyclists are competing in a race. In how many ways can the cyclists come in first, second, and third?
A combination lock will open when the right choice of five numbers (1-20) is selected. How many different lock combinations are possible?
3,200,000
(8!)/(6!)
56
How many distinguishable arrangements can be formed from the letters in the word BOOKKEEPER?
151,200
An electric train is moving north at 100 mph and a wind is blowing to the west at 10 mph. Which way does the smoke blow?
There is no smoke.
Six people volunteer to help put out a fire. In how many different ways can they be lined up in a row to hold the hose?
720
In Wyoming, each automobile license plate number consists of two capital letters followed by a four-digit number. How many distinct license plates can be formed?
6,760,000
(4!)/(0!)
24
How many distinguishable arrangements can be formed from the letters in the word TENNESSEE?
3,780
On my way to the fair, I met 7 jugglers and a bear leaving. Every juggler had 6 cats, every cat had 5 rats, every rat had 4 houses, every house had 3 mice, and every mouse had 2 lice. How many in all are going to the fair?
1
Mr. Ohler is electing a class president, vice president, and treasurer. If he has 8 students to choose from, in how many ways can the students be elected?
336
In Maine, each automobile license plate consists of two capital letters followed by a four-digit number. To avoid confusion, "O" and "zero" are not used. Neither are "I" and "one." How many distinct license plates can be formed in Maine?
2,359,296
(6!)/(2!*4!)
15
How many distinguishable arrangements can be formed from the letters in the word MATHEMATICS?
4,989,600
Mr. and Mrs. Smith have seven daughters. If each daughter has a brother, how many children do Mr. and Mrs. Smith have?
8
In how many ways can 10 children line up in a row?
3,628,800
How many different two-letter code words can be made from the letters a, b, c, d, and e if repetition of a letter is not allowed?
20
(7!*3!)/(6!*2!)
21
How many distinguishable arrangements can be formed from the letters in the word ALABAMA?
210
How could the 22nd and the 24th U.S. Presidents have the same parents, but weren't brothers?
It was the same person.
A group of 45 athletes is lining up to run a race. The top three runners earn gold, silver, and bronze medals. How many possible outcomes exist?
85,140
In how many ways can you answer a 12-question true/false exam? Assume that you do not omit any questions.
4,096
54/(4!-3!)
3
How many distinguishable arrangements can be formed from the letters in the word CONNECTICUT?
1,663,200
What letter comes next in the following sequence?
M, V, E, M, J, S, U, ___
N