John picks 3 different numbers between 10 and 20 inclusive. Assuming John picks randomly, what is the probability that John will pick the numbers 12 and 15 as two of his three selections?
Approach:
Probability = Total Desired Outcomes / Total Number of Outcomes
Total Number of Outcomes = 11c3 = 165
Total Desired =
12 and 15 must be in each set. So possibilities are:
12, 15, (any of the other 9) = 9 possibilities
12, (other 9), 15 = 9 possibilities
15, 12, (other 9) = 9 more
15, (other 9), 12 = 9 more
(other 9), 12, 15 = 9 more
(other 9), 15, 12 = 9 more
For a total of 9 x 6 = 54 desired; 54 / 165 = 18 / 55, not an option. Help!
A) 2/42
B) 3/55
C) 1/15
D) 4/36
E) 2/11
OA: B
Approach:
Probability = Total Desired Outcomes / Total Number of Outcomes
Total Number of Outcomes = 11c3 = 165
Total Desired =
12 and 15 must be in each set. So possibilities are:
12, 15, (any of the other 9) = 9 possibilities
12, (other 9), 15 = 9 possibilities
15, 12, (other 9) = 9 more
15, (other 9), 12 = 9 more
(other 9), 12, 15 = 9 more
(other 9), 15, 12 = 9 more
For a total of 9 x 6 = 54 desired; 54 / 165 = 18 / 55, not an option. Help!
A) 2/42
B) 3/55
C) 1/15
D) 4/36
E) 2/11
OA: B
