You are asked to create a 4-character password. Each character may be a letter or a number. How many different passwords are possible?
1,679,616
A waitress has five different entrees for the five people sitting at a table, but has forgotten which person ordered which entree. How many possible ways are there for her to serve the entrees?
120
A teacher has 28 students, and 5 of them will be chosen to participate in a play that has 5 distinct characters. How many different possible ways can the students be arranged in these roles?
11,793,600
How many different six-character passwords can be formed from the lowercase letters of the alphabet if repetition is not allowed?
165,765,600
A city council with seven members must elect a three- person executive committee consisting of a mayor, secretary, and treasurer. How many executive committees are possible?
210
Suppose you have 15 CDs from which you choose 6 CDs to put in the CD player in your car. If you are not particular about the order, how many 6-CD sets are possible?
5005
How many 6-person lineups can be formed from a 12-player volleyball roster, assuming every player can be assigned to any position?
665,280
How many license plates can be made of the form XX-YYYYY, where X is a letter of the alphabet and Y is a numeral.
67,600,000
How many different groups of seven balls can be drawn from a barrel containing balls numbered 1 -36?
8,347,680
How many different telephone numbers of the form aaa-bbb-cccc can be formed if an area code aaa cannot contain 0 and the prefix bbb cannot contain 9?
5,314,410,000
The debate club has 18 members, but only 4 can compete at the next meet. How many 4-person teams are possible?
3060
A recording engineer wants to make a CD with 12 songs. In how many different ways can the CD be made?
479,001,600
A dog shelter is giving away 15 different dogs, but you have room for only 4 of them. How many different dog families could you have?
1365
Find the probability that at least one other guest at a dinner party has your birthday if there are 12 people at the party
1/649,740
Find the probability of guessing the top three winners (in order) from a group of eight finalists in a soccer tournament.
1/336
Find the probability of choosing five lottery numbers that match five randomly selected balls when the balls are numbered 1 through 42.
1/850,668