Here are two question that I had trouble with, please provide some explanation:
Q#1
Five fair coins are tossed. What is the probability that exactly three of the coins land tails side up?
A 5/32
B 3/16
C 5/16
D 3/8
E 5/8
Q#2
A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
A 119
B 1,200
C 3,240
D 3,600
E 14,400
In the first question, I was able to obtain the answer by counting all combinations with 3 Tails, but I am having trouble finding a faster mathematical way of visualizing and solving the problem. The issue for me comes in determining the total number of combinations with 3 Tails facing up. In question two, again I could not figure out a straight forward way of dividing to remove the repeats. I would appreciate if someone could walk me through these. Thanks. Ans Q#1 C,Q#2 B
Source: Princeton Review Materials
Q#1
Five fair coins are tossed. What is the probability that exactly three of the coins land tails side up?
A 5/32
B 3/16
C 5/16
D 3/8
E 5/8
Q#2
A five-member committee is to be formed from a group of five military officers and nine civilians. If the committee must include at least two officers and two civilians, in how many different ways can the committee be chosen?
A 119
B 1,200
C 3,240
D 3,600
E 14,400
In the first question, I was able to obtain the answer by counting all combinations with 3 Tails, but I am having trouble finding a faster mathematical way of visualizing and solving the problem. The issue for me comes in determining the total number of combinations with 3 Tails facing up. In question two, again I could not figure out a straight forward way of dividing to remove the repeats. I would appreciate if someone could walk me through these. Thanks. Ans Q#1 C,Q#2 B
Source: Princeton Review Materials
