Ques 1:
Of 7 people, 4 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?
Soln 1:Shortcut:
no. of friendships = 5
total no. = 7C5 = 21
P (friends) = 5/21
So P (not friends) = 16/21 {Answer is correct}
Ques 2.
Of 9 people, 6 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?
Soln 2:Shortcut:
no. of friendships = 6
total no. = 9C6 = 84
P (friends) = 6/84= 1/14
So P (not friends) = 13/14 {incorrect}
Actually the no. of friendships should come equal to 7, so that 9C7= 36 & P(f) = 1/6 & P(nf)=5/6 {correct}
What mistake am I making in ques 2? or is the short cut method only not universal? Pls help. Thnks
Of 7 people, 4 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?
Soln 1:Shortcut:
no. of friendships = 5
total no. = 7C5 = 21
P (friends) = 5/21
So P (not friends) = 16/21 {Answer is correct}
Ques 2.
Of 9 people, 6 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?
Soln 2:Shortcut:
no. of friendships = 6
total no. = 9C6 = 84
P (friends) = 6/84= 1/14
So P (not friends) = 13/14 {incorrect}
Actually the no. of friendships should come equal to 7, so that 9C7= 36 & P(f) = 1/6 & P(nf)=5/6 {correct}
What mistake am I making in ques 2? or is the short cut method only not universal? Pls help. Thnks
