http://www.ck12.org Chapter 2. Conditional Probability
Democrats:18 C 3 =18!
3!( 18 − 3 )!
18 C 3 =
18!
3!( 15 )!
18 C 3 =
18 × 17 × 16
3 × 2 × 1
18 C 3 =
4 , 896
6
18 C 3 =^816
From the 20 Republicans(n= 20 )in the committee, we are choosing 4(r= 4 ).
Republicans:20 C 4 =20!
4!( 20 − 4 )!
20 C 4 =
20!
4!( 16 )!
20 C 4 =
20 × 19 × 18 × 17
4 × 3 × 2 × 1
20 C 4 =
116 , 280
24
20 C 4 =^4 ,^845
Therefore, the number of ways the committee can form a sub-committee consisting of 3 Democrats and 4 Republi-
cans is:
Total combinations= 18 C 3 × 20 C 4 = 816 × 4 , 845 = 3 , 953 , 520
Practice
- Determine whether the following situations would require calculating a combination:
a. Selecting 3 students to attend a conference in Washington, D.C.
b. Selecting a lead and an understudy for a school play
c. Assigning students to their seats on the first day of school - In how many ways can you select 17 songs from a mix CD of a possible 38 songs?
- If an ice cream dessert can have 2 toppings, and there are 9 available, how many different selections can you
make? - If there are 17 randomly placed dots on a circle, how many lines can be formed using any 2 dots?
- A committee of 4 is to be formed from a group of 13 people. How many different committees can be formed?
- There are 4 kinds of meat and 10 veggies available to make wraps at the school cafeteria. How many possible
wraps have 1 kind of meat and 3 veggies? - There are 15 freshmen and 30 seniors in the Senior Math Club. The club is to send 4 representatives to the
State Math Championships.
a. How many different ways are there to select a group of 4 students to attend the State Math Champi-
onships?