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#12 assignment2

A city council consists of 5 Democrats and 6 Republicans. If a committee of 6 people is​ selected, find the probability of selecting 3 Democrats and 3 Republicans.

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​(Type a fraction. Simplify your​ answer.)

User Vibol
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1 Answer

3 votes

Answer:

200/462 = (2100)/(2231) = 100/231

Explanation:

To find the probability of selecting 3 Democrats and 3 Republicans out of a committee of 6 people, we need to use the combination formula:

C(n,r) = n! / (r! * (n-r)!)

where n is the total number of people, r is the number of people we want to select, and C(n,r) represents the number of possible combinations.

The total number of possible committees of 6 people that can be formed from a city council of 11 members is:

C(11,6) = 11! / (6! * (11-6)!) = 462

Now we need to find the number of committees with 3 Democrats and 3 Republicans. We can choose 3 Democrats from the 5 Democrats in C(5,3) ways, and 3 Republicans from the 6 Republicans in C(6,3) ways. So the number of committees with 3 Democrats and 3 Republicans is:

C(5,3) * C(6,3) = 10 * 20 = 200

Therefore, the probability of selecting 3 Democrats and 3 Republicans from a committee of 6 people is:

P = 200 / 462 = 0.4329 or 43.29% (rounded to four decimal places)

User Mhluzi Bhaka
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