Consider three groups, group A, group B, and group C, each consisting of ten peo

Question

Consider three groups, group A, group B, and group C, each consisting of ten people. A subgroup of three people is to be selected from the combined group of thirty people. a) How many choices of three people are possible? b) How many choices of three people are there in which all three people come from group A? c) How many choices of three people are there in which all three people come from the same group of ten? d) How many choices of three people are there in which one of the three people comes from group A, one comes from group B, and one comes from group C?

Explanation / Answer

1) Required no . of choices = 30C3 = 30*29*28/6 = 4060

2) Required no . of choice = 10C3 = 10*9*8/(1*2*3) = 120

3) Required no. of ways = 3 * 10C3 = 3*120=360

4) Required no. of ways = 10* 10*10 = 1000

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