A rectangle is divided into eight equal parts, two parts are shaded. What fraction is equivalent to the area of the rectangle?
2 answers:
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Answer:
choices
Step-by-step explanation:
We know that we'll have to solve this problem with a permutation or a combination, but which one do we use? The answer is a combination because the order in which the child picks the candy <u><em>does not</em></u> matter.
To further demonstrate this, imagine I have 4 pieces of candy labeled A, B, C, and D. I could choose A, then C, then B or I could choose C, then B, then A, but in the end, I still have the same pieces, regardless of what order I pick them in. I hope that helps to understand why this problem will be solved with a combination.
Anyways, back to the solving! Remember that the combination formula is
, where n is the number of objects in the sample (the number of objects you choose from) and r is the number of objects that are to be chosen.
In this case, and
. Substituting these values into the formula gives us:
(Expand the factorials)
(Cancel out
)
(Evaluate denominator)
(Cancel out
)
Therefore, the child has different ways to pick the candies. Hope this helps!