Question

6. There is party of 2000 people in that party. Think that each person knows 200 other people at the party and it is random and Relation is mutual, if C knows D then D also knows C.

(a) What is the probability that 4 random chosen people know one and other(him self and other person)?

(b) What is the probability that 4 random chosen people do't know one and other(him self and other person) and do not have mutual Relation .

(c) What is the probability that 4 randomly chosen people do't know one and other(him self and other person) and have mutual Relation.

Answer 1

Solution:

a) P( 4 randomly choosen people know one and other) = (2000C1 200C3)/2000C4

b) P( 4 randomly chosen people don't know one and other and do not have mutal relation)

= 1 - P( 4 randomly choosen people know one and other)

   = 1 - ((2000C1 200C3)/2000C4)

c)P( 4 randomly chosen people don't know one and other and do have mutal relation) = 0

As if the person don't know one and other then he can't have a mutal relation, so this case is impossible, hence zero probability of occuring.