2.2. Permutations and Combinations Compared http://www.ck12.org
b. In this problem, there are 10 committee members to choose from, son=10. We want to choose 3 members to be
president, vice-president, and treasurer; therefore, we are choosing 3 objects at a time. In this example,r=3.
nPr=n!
(n−r)!10 P 3 =10!
( 10 − 3 )!
10 P 3 =
10!
7!
=
10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
7 × 6 × 5 × 4 × 3 × 2 × 1
10 P 3 =
720
1
10 P 3 =^720
Practice
- Solve for 7 P 5.
- Evaluate 4 P 2 × 5 P 3.
- How many different 4-digit numerals can be made from the digits of 56987 if a digit can appear just once in a
numeral? - In how many ways can 6 students be chosen from 9 students if the order in which the students are chosen
matters? - A TV station has 8 hour-long TV shows to choose from in order to fill 2 one-hour time slots. In how many
ways can it fill the time slots? - A basketball league consists of 12 teams. In how many ways can the teams finish in first, second, and third
place? - A secret code consist of 3 digits from 0 to 9 followed by 2 letters from ’A’ to ’Z’. None of the digits or letters
repeat. How many secret codes are possible? - On a test, Robert has been presented with 15 vocabulary words and 15 definitions. He is being asked to match
each vocabulary word to the appropriate definition. How many different ways are there for Robert to do the
matching? - A couple just had twin boys, but they can’t decide between the names Mike, Mark, Peter, Paul, Sam, and
Sonny. If the couple randomly chooses names for the 2 boys from the names listed, what is the probability
that the first boy born will be named Sam and the second boy born will be named Mark? Assume that the boys
will not have the same name. - For question 9, what is the probability that one of the boys will be named Peter and the other boy will be
named Paul?