GATE 2017 EC

Question

Q1. Three indian and three chinese split into subgroups having atleast one indian. How many subgroups are possible?

Comments

Sir, good evening. I got 52 as the answer. Here is the explanation.

Total no of subgroups with atleast one Indian = 3c1(3c1+3c2+3c3)+3c2(3c0+3c1+3c2+3c3)+3c3(3c0+3c1+3c2).  =  52

A subgroup consists of max 5 members and min 2 members out of 6 members.

Answer 1

1 indian && (0 or 1 or 2 or 3) chinese = ³C₁ × [³C₀ + ³C₁ + ³C₂ + ³C₃] = 3 × [8]

2 indian && (0 or 1 or 2 or 3) chinese = ³C₂ × [³C₀ + ³C₁ + ³C₂ + ³C₃] = 3 × [8]

3 indian && (0 or 1 or 2 or 3) chinese = ³C₃ × [³C₀ + ³C₁ + ³C₂ + ³C₃] = 1 × [8]

Total sets = 8× (3+3+1) = 56

Comments

@Akash in that case you are taking redundant cases: say A B C from India and E F G from China , you take A always now from rest 5 you take B, E , now you take  B always and from rest 5 you take A, E . So here comes the redundancy ..

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sir,If we select one indian and zero chineese it means we are selecting a single person but a subgroup means atleast two members right. And one more thing if we select 3 indians and 3 chineese means we are selecting whole group but not subgroup

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@Shreya

I didn't get ur comment.plzz explain elaborately.mine also coming 52