Permutation, Combination and Fundamental Counting Principle Practice
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1) From 8 shirts, 6 pairs of slacks and 4 jackets, how many different outfits can be made?
2) There are 11 questions on a true/false test. If all questions are answered, in how many different ways
can the test be completed?
3) Find the number of permutations of the letters c, a, r, b, o, n.
4) How many ways can 11 books be arranged on a book shelf?
5)
Determine if each situation is a permutation or combination. a.) choosing 2 Senators b.)a 3-digit lock
combination c.)1st, 2nd, and 3rd chairs d.)a hand of five cards
6) How many groups of 6 crayons can be selected from a box of 24 crayons?
7) The manager of a baseball team wants the best hitter up fifth. If the lineup consists of 9 players, how
many different lineups are possible?
8) How many 3 letter code words can be made from the letters b, c, d, e, and f, if repetition of a letter is
allowed?
9) How many 4-element subsets can be formed from the set {a, b, c, d, e, f, g}?
10) How many different committees of 3 can be chosen from 12 people?
11) There are 14 different pens in a carton. How many different sets of 11 pens can be chosen?
12) There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four
representatives to the State Conference. If the members of the club decide to send two juniors and
two seniors, how many different groupings are possible?
13) How many 2 digit numbers can you make using the digits 1, 2, 3 and 4 without repeating the digits?
14) How many 3 letter “words” can you make out of the letters CRAZY?
15) In a lottery, 4 winners will get equal prizes. If 20 people enter the lottery, how many different groups
of 4 winners can be chosen?
16) Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his
next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9 th
quiz?
17) Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85%
of its previous height. How high will the ball rebound after its third bounce? Round to the nearest
tenth.
18) Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans
to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how
many baskets will she have to sell?
19) A ball is dropped from a table that is twenty‐four inches high. The ball always rebounds three fourths
of the distance fallen. Approximately how far will the ball have traveled when it finally comes to rest?
20) A grocery store display of soup cans has sixteen rows with each row having one less can than
the row below it. If the bottom row has twenty‐eight cans, how many cans are in the display?
Permutation, Combination and Fundamental Counting Principle Practice
1) From 8 shirts, 6 pairs of slacks and 4 jackets, how many different outfits can be made?
8*6*4=192
2) There are 11 questions on a true/false test. If all questions are answered, in how many different ways
can the test be completed?
2^11=2048
3) Find the number of permutations of the letters c, a, r, b, o, n.
6P6=720
4) How many ways can 11 books be arranged on a book shelf?
11!=39,916,800
5) Determine if each situation is a permutation, combination, or neither.
a.)
choosing 2 Senators C
b.)
a 3-digit lock combination P
st
nd
rd
c.)
1 , 2 , and 3 chairs P
d.)
a hand of five cards C
6) How many groups of 6 crayons can be selected from a box of 24 crayons?
24C6 = 134,596
7) The manager of a baseball team wants the best hitter up fifth. If the lineup consists of 9 players, how
many different lineups are possible?
8!= 40,320
8) How many 3 letter code words can be made from the letters b, c, d, e, and f, if repetition of a letter is
allowed?
5^3 = 125
9) How many 4-element subsets can be formed from the set {a, b, c, d, e, f, g}?
7C4 = 35
10) How many different committees of 3 can be chosen from 12 people?
12C3 = 220
11) There are 14 different pens in a carton. How many different sets of 11 pens can be chosen?
14C11 = 364
12) There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four
representatives to the State Conference. If the members of the club decide to send two juniors and
two seniors, how many different groupings are possible?
14C2 * 23C2 = 23,023
13) How many 2 digit numbers can you make using the digits 1, 2, 3 and 4 without repeating the digits?
4P2 = 12 This is a permutation because 43 doesn’t equal 34 so order matters
14) How many 3 letter “words” can you make out of the letters CRAZY?
5P3 = 60
This is a permutation because ZAY is not the same as YAZ
15) In a lottery, 4 winners will get equal prizes. If 20 people enter the lottery, how many different groups
of 4 winners can be chosen?
20C4 = 4,845
16) Edgar is getting better at math. On his first quiz he scored 57 points, then he scores 61 and 65 on his
next two quizzes. If his scores continued to increase at the same rate, what will be his score on his 9th
quiz?
57 + (9-1)(4) = 89
17) Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85%
of its previous height. How high will the ball rebound after its third bounce? Round to the nearest
tenth.
15(.85)^(4-1) =9.2
18) Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans
to make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how
many baskets will she have to sell?
13 + (16-1)(12) = 193
19) A ball is dropped from a table that is twenty‐four inches high. The ball always rebounds three fourths
of the distance fallen. Approximately how far will the ball have traveled when it finally comes to rest?
168
20) A grocery store display of soup cans has sixteen rows with each row having one less can than
the row below it. If the bottom row has twenty‐eight cans, how many cans are in the display?
328