kirankp wrote:
If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible?
A. 20
B. 40
C. 50
D. 80
E. 120
Take the task of creating a committee and break it into
stages.
Stage 1: Select 3 COUPLES
Since the order in which we select the couples does not matter, we can use COMBINATIONS
We can select 3 couples from 5 couples in 5C3 ways ( =
10 ways)
ASIDE: If anyone is interested, we have a video on calculating combinations (like 5C3) in your head (see bottom of post)At this point, we have selected 3 COUPLES, which we'll call A, B and C. We're now going to select ONE person
from each couple to be on the committee.
Stage 2: Select 1 person from couple A
There are 2 people in this couple, so we can complete this stage in
2 ways.
Stage 3: Select 1 person from couple B
There are 2 people in this couple, so we can complete this stage in
2 ways.
Stage 4: Select 1 person from couple C
There are 2 people in this couple, so we can complete this stage in
2 ways.
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create a 3-person committee) in
(10)(2)(2)(2) ways (= 80ways)
Answer:
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