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OpenStudy (anonymous):

Suppose that 3 of the 200 people who answered a survey are selected to win a travel bag as a thank-you gift. How many different ways could the selection of 3 people be made?

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OpenStudy (anonymous):

\[\dbinom{200}{3}=\frac{200\times 199\times 198}{3\times 2}\]

OpenStudy (anonymous):

what is in the parenthesis?

OpenStudy (anonymous):

\[=200\times 199\times 33=1313400\]

OpenStudy (anonymous):

read "200 choose 3" the number of ways to choose 3 from a set of 200

OpenStudy (anonymous):

it really just restates the question. the arithmetic on the right gives the answer

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OpenStudy (anonymous):

ohh ok got it ;)

OpenStudy (anonymous):

reason as follows: 200 choices for one prize then 199 for the second and 198 for the third, but then divide by 6 because that is how many ways you can reorder the 3 people, and you only want to count once

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