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In a state legislature the elected representatives include 1717 Democrats,1111 Republicans, and 33 .Independents.​ What's the...

In a state legislature the elected representatives include 1717 Democrats,1111 Republicans, and 33 .Independents.​ What's the probability that a random selection of 6 legislators would include 2 of​ each?

Math   Statistics-And-Probability   
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Answer #1

Answer: In a state legislature the elected representatives include 17 Democrats,11 Republicans, and 3 .Independents.

​ What's the probability that a random selection of 6 legislators would include 2 of​ each?

Solution:

Total legislature = 17 + 11 + 3 = 31

a random selection of 6 legislators

31C6 = 31! / 6! * 25!

31C6 = 736281

Includes 2 of each

Democrats = 17C2 = 136

Republicans = 11C2 = 55

Independents = 3C2 = 3

Therefore,

required probability = (17C2 * 11C2 * 3C2) / 31C6

= 136 * 55 * 3 / 736281

= 22440/736281

= 0.030477

= 0.0305

Therefore, the probability that a random selection of 6 legislators include 2 of​ each would be 0.0305.

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