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3-4 Practice FCP and Permutations

Last updated almost 8 years ago
20 questions
Note from the author:
Fundamental Counting Principle and Permutations Practice
Type in the equation you use to solve the problem = answer.
Ex: 7*4*2=56
8P3=336
9!/(2!3!)=30240
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1) At the after school Hawk Club meeting, there were four drinks you could choose from: orange soda, Coke, Dr. Pepper, and water. There were three snacks you could choose from: peanuts, fruit, and cookies. Each student may have only one drink and one snack.
Use the counting principle to find the number of choices available

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2) How many different choices are available for a car if there are 4 different body styles, three different types of engines, and 10 different colors?
3) How many different passwords can be made if it is three letters, followed by two digits, followed by a letter? (Repetition is allowed)
4) How many different license plates can be made if it is one letter, followed by two digits, followed by two letters if no letter or number can be repeated?
5) The ski club has ten members to choose three officers (captain, co-captain, and secretary) from. How many ways can those offices be filled?
6) How many different ways can the word REFEREE be arranged?
7) How many different ways can the word ELEMENTARY be arranged?
8) 10!
8!2!
9) 7P5
10) 8P5
6 P3
11) 8P3 * 4P2
12) How many ways can 1st place, 2nd place, and 3rd place be chosen if there are 55 contestants in the beauty pageant?

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3) How many different passwords can be made if it is three letters, followed by two digits, followed by a letter? (Repetition is allowed)

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4) How many different license plates can be made if it is one letter, followed by two digits, followed by two letters if no letter or number can be repeated?

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5) The ski club has ten members to choose three officers (captain, co-captain, and secretary) from. How many ways can those offices be filled?

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6) How many different ways can the word REFEREE be arranged?

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7) How many different ways can the word ELEMENTARY be arranged?

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8) 10!
8!2!

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9) 7P5

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10) 8P5
6 P3

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11) 8P3 * 4P2

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12) How many ways can 1st place, 2nd place, and 3rd place be chosen if there are 55 contestants in the beauty pageant?

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The batting order for eight players on a 10
person team.

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The student body of 125 students wants to
elect a president, vice president, and
secretary.

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16 teams are in the Sweet 16 tournament. 2 of them will end up in 1st and 2nd place. How many ways can this happen?

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The batting order for nine players on a 12
person team.

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Castel and Joe are planning trips to three
countries this year. There are 7 countries
they would like to visit. One trip will be
one week long, another two days, and the
other two weeks.

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The student body of 10 students wants to
elect a president, vice president, secretary,
and treasurer.

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The five Smith children run to the ice cream truck. How many ways can they line up to order?

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A volleyball squad has twelve players.
How many ways can the players line up to greet the opposing team?