SOLUTION: Ten students, A, B,..., are in a class. A committee of three is chosen at random to represent the class. Find the probability that: (a) A belongs to the committee; (b) B belong

Question 1119078: Ten students, A, B,..., are in a class. A committee of three is chosen at random to represent the class. Find the
probability that:
(a) A belongs to the committee;
(b) B belongs to the committee;
(c) A and B belong to the committee;
(d) A or B belong to the committee;
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
Ten students, A, B,..., are in a class. A committee of three is chosen at random to represent the class. Find the
probability that:

Of 10 students of the class, you can form   =  = 120 triples (triplets), in all.



(a) A belongs to the committee;        You can form   = 36 such triples, by adding two other of remaining 9

                                       students of the class.

                                       So the probability under the question is   =  = 0.3 = 30%



(b) B belongs to the committee;        Same answer (and same solution) as (a).




(c) A and B belong to the committee;   You can form only 8 such triples by adding any of remaining 8 students to A and B.

                                       The answer is   = .



(d) A or B belong to the committee;    Add (a) with (b) and subtract (c):

                                        =  =  = .

Solved.

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