Re: Joshua and Jose work at an auto repai

Lets see if I can help here:

First of all a bit of theory:

Combinations : the order is NOT relevant
What do I mean? Changing the order DOES NOT result in a new arrangement

Example Combinations:"select a team of 5 from a group of 10". In this case the team remains the same and is not affected by the order I choose the players
To make it clear under there is an example of Perutaions is which the order IS important
I don't wanna confuse you but I think it's important to know the difference
Example Premutation: the very classic "How many ways can 5 students be arranged in a row of 10"? In this case the order is important

Now lets see the formulas
N= numb items, K=spots
Tot combinations= \frac{n!}{k!(n-k)!}

Now down to the questions:
1)From a group of 5 managers (Joon, Kendra, Lee, Marnie and Noomi), 2 people are randomly selected to attend a conference in Las Vegas. What is the probability that Marnie and Noomi are both selected?
(A) 0.1
(B) 0.2
(C) 0.25
(D) 0.4
(E) 0.6

The order is not important (M and N = N and M at the conference) in this case => Comb
Tot cases=\frac{5!}{3!2!}=10 case "good" M,N (or N,M order Not imp) so \frac{1}{10}

2)Joshua and Jose work at an auto repair center with 4 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
a)1/15
b)1/12
c)1/9
d)1/6
e)1/3

The order is not important => Comb
Tot cases=\frac{6!}{2!4!}=15 case good Josh,Jose (or Jose,Josh order Not imp) so \frac{1}{15}

I suggest you to use this approach to solve questions like those
However from a probability point of view:

This means that P(M and N both selected) = (2/5) x (1/4) = 1/10
2/5 Means one of the two (2 out of 5), 1/4 means the other

(1/6)*(1/5)+(1/6)*(1/5)=2/30=1/15
Here 1/6 and 1/5 are singular and for this must be taken twice. please note the difference
In the first we have (one of the two)*(the other). This already contains the "other way"
In the second we have (Josh)*(Jose), but this does not contain the "other way". That's why also (Jose)*(Josh) must be taken into consideration
If we solve the second as the first we would get:
2/6*1/5=1/15 => same approach as one (one of the two)*(the other)

(Tip: use comb are more clear )

Sorry for the lenght of the post but I felt like clarity>synthesis here
Hope it's clear. Let me know