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In a room filled with 7 people ,4 people have exactly 1 Sibling in the room and three people have exactly two sibling in the room .if two individuals are selected from the room at random what is the probability that those two individuals are not sibling?

5/21

3/7

4/7

5/7

16/21
asked in Combinatory by Active (1.8k points)   | 26 views
16/21

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Assume every person to be vertex and no of sibling be the degree of vertex 

so the degree sequence will be {1,1,1,1,2,2,2}   for the vertices let's say {A,B,C,D,E,F,G}

one of the graphs possible is A is the sibling of B and vice versa(there exists edge between A and B ), C is the sibling of D and vice versa (there exists edge between C and D),  E, F, and G are siblings of each other(there exists edge between every possible pair of E,F and G).

P(selecting a pair of persons which are siblings)=( C(2,2)(for the A and B case)+C(2,2)(for the C and D case)+C(3,2)(for the E,F and G case))/C(7,2)(for all possible pairs)

=(1+1+3)/21 = 5/21

required probability = 1-(5/21)=16/21

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