I have a few problems I was wondering I was doing them right. Here they are:
1) In how many ways can 5 starting positions on a basketball team be filled with 10 men whom can play any position.
C(10,5) = 252
2) Nine people are going on a skiing trip in 3 cars that can hold 2, 4, and 5 passengers, respectively. In how many ways is it possible to transport nine people to the ski logde using all cars?
P(2,2)*P(4,4)*P(5,3) = 2*24*60 = 2880
3) The Detroit Music Company has purchased the rights to 10 different songs and it plans to release a new cd with 5 of them.
a) How many different cds are possible if the order of songs is important?
b) not important?
a)P(10,5) = 30,240
b)C(10,5) = 252
4) From a group of 4 men and 5 women, how many committees of size 3 are possible
a) with no restrictions?
b) with 1 man and 2 women?
c) with 2 men and 1 woman if a certain man must be on the committee?
a)C(9,6) = 84
b)C(4,1) * C(5,2) = 4 * 10 = 80
c)P(4,1) * C(3,1) * C(5,1) = 4 * 3* 5 = 60
5) Wood County sheriff classifies crimes by age (in years) of criminal and whether the crime is violent or nonviolent. As shown below, a total of 150 crimes were reported by the sheriff last year.
20 to 40
40 or older
a)What is the probability of selecting a case to analyze and finding it involved a violent crime?
b)What is the probability of selecting a case to analyze and finding the crime was committed by someone less than 40 years old?
c)What is the probability of selecting a case that involved a violent crime or an offender less than 20 years old?
d)Given that the violent crime is seleced for analysis, what is the probability the crime was committed by a person under 20 years old?
e)Two crimes are seleced by a Judge. What is the probability both are violent crimes?
C)C(150,82) * C(150,12)
E)C(150,82) * C(150,81)
Sorry for all the problems. I just want to make sure I am doing these right. Thanks