(=
Is one thing better ? If So=P.
Name
Permutations vs Combinations
Date
Period
State if each scenario involves a permutation or a combination.
1) A team of 8 basketball players needs to
2) Rob and Mary are planning trips to nine
choose a captain and co-captain.
countries this year. There are 13 countries
they would like to visit. They are deciding
nPr
which countries to skip.
8/2=56
nCr
13Cq=715
3) The batting order for seven players on a 12
4) There are 45 applicants for three Computer
Programmer positions.
person team.
nCr
in
12C7=792
*
Just get hired"
Just
be
nCr 45 C3= = 14,190
Medical
State if each scenario involves a permutation or a combination. Then find the number of
possibilities.
5) Castel and Joe are planning trips to three
6) There are 110 people at a meeting. They
countries this year. There are 7 countries
each shake hands with everyone else. How
they would like to visit. One trip will be
many handshakes were there?
one week long, another two days, and the
other two weeks.
7P3 210time one factor is better
nCr never shake same
hand twice
"ay "
ne
nPr
110C2=5,995
(4x3)(2y)
7) You are setting the combination on a
8) A group of 25 people are going to run a
three-digit lock. You want to use the
race. The top 8 finishers advance to the
numbers 123 but don't care what order they
finals.
10
are in.
nPr
2518
sps=4.36x10
nPr 3/3
9) A team of 17 softball players needs to
10) 5 out of 13 students will ride in a car
choose three players to refill the water
instead of a van
cooler.
13C5=1,287
nCr 17C3=680
nGr
11) The student body of 10 students wants to
12) Selecting which seven players will be in the
elect a president, vice president, secretary,
batting order 11 person team.
on a
iiC7
and treasurer.
10P4=5,040
nCr Just be in = 330
nPr
13) There are 15 applicants for four jobs:
14) A group of 45 people are going to run a
Computer Programmer, Software Tester,
race. The top three runners earn gold,
sky24
Manager, and Systems Engineer.
silver, and bronze medals.
15P4=32,760 =
451 sp=85,140
nPr
if one job is
nPr
better.
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