There are three Democrats and four Republicans in a group of seven people. If tw

Question

There are three Democrats and four Republicans in a group of seven people. If two people are selected from the total of seven, how many ways can two Democrats be selected?

There are three Democrats and four Republicans in a group of seven people. If two people are selected from the total of seven, how many ways can two Democrats and one Republican be selected?

There are three Democrats and four Republicans in a group of seven people. If two people are selected from the total of seven, how many ways can two people be selected?

Please show how you got the answers. Thanks!

Explanation / Answer

Combination formula, nCr = n! / (r! x (n-r)!)

3 Democrats and 4 Republicans

a) If two are selected, number of ways in which two democrats can be selected = 3C2 = 3

b) If two are selected, number of ways in which one democrat and one republican can be selected

= 3C1 x 4C1

= 3 x 4

= 12

c) Number of ways in which 2 people can be selected from 7 = 7C2

= 7! / (2! x (7-2)!)

= 21

P.S: In part two, if the question was, If three people are selected from the total of seven, how many ways can two Democrats and one Republican be selected

= 3C2 x 4C!

= 3 x 4

= 12

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