Question 1055966: Ted has a cat carrier which will hold 3 cats. Unfortunately, Ted has 5 cats: Muffy, Nero, Oprah, Penny, and Quade.
a. Make an organized list to show all the ways Ted can chose 3 cats at random to put in the cat carrier. My answer: 5 x 4 x 3 = 60 I am not sure how to make a list.
b. How many of the ways in part (a) contain Oprah?
c. How many ways in part (b) contain both Muffy and Nero.
d. Based on your answers to parts (a) and (b) what is the probability that Oprah will end up in the cat carrier?
Found 3 solutions by stanbon, addingup, jim_thompson5910:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Ted has a cat carrier which will hold 3 cats. Unfortunately, Ted has 5 cats: Muffy, Nero, Oprah, Penny, and Quade.
a. Make an organized list to show all the ways Ted can chose 3 cats at random to put in the cat carrier.
Ans: 5C3 = (5*4)/(1*2) = 10 ways
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MNO; MNP; MNQ; MOP; MOQ; MPQ ; NOP; NOQ; NPQ; OPQ
b. How many of the ways in part (a)
contain Oprah?
Ans: 5
c. How many ways in part (b) contain both Muffy and Nero.
Ans: 1
d. Based on your answers to parts (a) and (b) what is the proba
bility that Oprah will end up in the cat carrier?
Ans: 5/10 = 1/2
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Cheers,
Stan H.
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Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! So, we have a combination where the order doesn't matter. And we'll pick a group of 3 out of a population of 5:
n = total of 5
k = group of 3
C(5, 3) = n!/((n-k)!k!)
= 5!/((5-3)!3!)
= 5!/(2!*3!)
= 120/12 = 10 possible combinations.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Let,
M = Muffy
N = Nero
O = Oprah
P = Penny
Q = Quade
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(a)
5*4*3 = 60
There are 60 ways to do this if order mattered, but it doesn't. So we divide by 6. Why 6? Because there are 6 ways to order any 3 individuals (3! = 3*2*1 = 6).
60/6 = 10
So the final answer to part (a) is 10. The list would be
M,N,O
M,N,P
M,N,Q
M,O,P
M,O,Q
M,P,Q
N,O,P
N,O,Q
N,P,Q
O,P,Q
each line represents a different combination. Something like M,N,O is the same as M,O,N or N,M,O since they have the same 3 cats just in a different order. Order does not matter. As you can see in the list above, there are 10 different combinations.
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(b)
Hold one slot to have it fill Oprah (O). There are 2 slots left with 4 choices to fill it
4 C 2 = (4 P 2)/(2!) = (4*3)/2 = 12/2 = 6
There are 6 ways to do this
If you look at the list in part (a), you'll see these entries that have O in them somehow
M,N,O
M,O,P
M,O,Q
N,O,P
N,O,Q
O,P,Q
There are 6 of those entries listed above. So however you do it, the final answer to part (b) is 6
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(c)
Look at the list in part (b). Look for entries that have both M and N together at the same time. It only happens once and it is M,N,O
The final answer to part (c) is 1
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(d)
In part (a), the answer is 10
In part (b), the answer is 6
There are 6 ways to get what we want (have Oprah picked) out of 10 ways total
Simply divide the two values to get
6/10 = 3/5 = 0.6
The final answer as a fraction is 3/5. Don't forget to reduce fully.
The final answer in decimal form is 0.6
The final answer as a percentage is 60%
The way you report the answer will depend on your teacher's instructions.
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