Jenna has a bag of 4 marbles: 1 red, 1 blue, 1 green, and 1 purple. Make a sample space for Jenna picking two marbles. How many outcomes are there?
A 4
B 6
C 8
D 12
E 16
Jenna has a bag of 4 marbles: 1 red, 1 blue, 1 green, and 1 purple. Make a sample space for Jenna picking two marbles. How many outcomes are there?
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To determine the number of outcomes when Jenna picks two marbles from a bag of four different colors (red, blue, green, and purple), we can use the combination formula since the order in which she picks the marbles does not matter.
The formula for combinations is given by:
[
text{C}(n, r) = frac{n!}{r!(n – r)!}
]
Where:
– ( n ) is the total number of items (in this case, 4 marbles).
– ( r ) is the number of items to choose (in this case, 2 marbles).
Plugging in the numbers:
[
text{C}(4, 2) = frac{4!}{2!(4 – 2)!} = frac{4!}{2! cdot 2!} = frac{4 times 3}{2 times 1} = 6
]
Thus, there are 6 possible combinations for picking 2 marbles from 4, which correspond to the following pairs: (red, blue), (red, green), (red, purple), (blue, green), (blue, purple), and (green, purple).
Therefore, the correct answer is B 6.