SOLUTION: 2) In a pen are 2 beagles, 2 golden retrievers, and 1 cocker spaniel. If 2 of the dogs are chosen at random, what is the sample space (all possible combinations )? What is the prob

Question 249399: 2) In a pen are 2 beagles, 2 golden retrievers, and 1 cocker spaniel. If 2 of the dogs are chosen at random, what is the sample space (all possible combinations )? What is the probability of choosing 2 dogs of the same breed?

I'm thinking the outcomes is 20, so it would be 2/20 or 1/10?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
1/10 is 2/20 reduced
On this page we hope to clear up problems you might have with probability and things related to it, such as factorials and sigma notation. Sigma notation is especially useful to know because you use it a lot in calculus when you find area under curves. Click any of the links below or scroll down to better your understanding of probability.
Sigma notation
Permutations
Combinations
Probability
Quiz on Probability
Sigma Notation
Σ, the Greek letter sigma (if you have an old browser that can't display Sigma, it looks like a mix between an E and a Z), can be used to simplify sequences of numbers. The sum of terms in the sequence is found using sigma notation (also called summations). Example:

1. Problem: 4
Σ (2k + 1)
k = 1
Solution: This is a sum of (2k + 1) from
1 to 4.
Plug all numbers from 1 to 4 into
the general term ((2k + 1) in this case)
and then add the terms together.
(2(1) + 1) = 3
(2(2) + 1) = 5
(2(3) + 1) = 7
(2(4) + 1) = 9
3 + 5 + 7 + 9 = 24
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Permutations
A permutation of a set of objects is an arrangement of the objects in a certain order. For example, take the set of four objects {pepperoni, sausage, onions, mushrooms}. They can be arranged on a pizza many different ways. Below are a few of the ways.
pepperoni, sausage, onions, mushrooms
sausage, onions, mushrooms, pepperoni
onions, mushrooms, pepperoni, sausage
mushrooms, pepperoni, sausage, onions
pepperoni, sausage, mushrooms, onions
There are some more, but we won't list them. To find the number of different arrangements of the set we select a first choice; there are 4 possible choices. Now we take a second choice; there are 3 choices. Now pick a third choice; there are 2 choices. Finally, there is 1 choice for the last selection. Thus, there are 4 * 3 * 2 * 1 or 24 different ordered arrangements of the toppings. This product can also be written as 4! (read: 4-factorial).
The total number of permutations of a set of n objects is given by n!. Example:
1. Problem: 5!
Solution: 5 * 4 * 3 * 2 * 1
120
When you have a set of objects and only want to arrange part of them, you have a permutation of n objects r at a time. For example, if you have 6 toppings for a pizza, and a customer calls and tells you to put any 3 toppings on the pizza, you might want to know how many different pizzas you can make. You can select the first topping in 6 ways, the second in 5, and the third in 4. As we learned above, this can be written as 6 * 5 * 4. There is a theorem that tells us about a formula for the situation above. It says the number of permutations of a set of n objects taken r at a time is given by the following formula: nPr = (n!)/(n - r)!. Example:
second part
I don't have any idea where you got 10 nor 20!!
how many dogs are you choosing ?
add up the number of dogs
that will be you second number
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