SOLUTION: In how many ways can a committee of 7 be formed if there are 10 dogs and 15 cats to choose from and the committee must consist of at least 1 cat?

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Question 352191: In how many ways can a committee of 7 be formed if there are 10 dogs and 15 cats to choose from and the committee must consist of at least 1 cat?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Hi,
*Note: The probability of x successes in n trials is:
.
P = nCx* p%5Ex*q%5E%28n-x%29 where p and q are the probabilities of success and failure respectively.
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nCx = n%21%2F%28x%21%28n-x%29%21%29
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Question states p(dog drawn) = 10/25 0r .4 and q (cat drawn) = .6
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Probability (At least 1 cat) = 1 - P(no cats)
P(no cats)
7C7 = +7%21%2F%287%21%2A0%21%29%21=+1+
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P(no cats) = 1%2A%28.4%29%5E7%2A%28.6%29%5E0 = .0016
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1 - P(no cats) = .9983