The question is really simple - I want to check whether my method of solving the question is correct.
Typical solution -
Number total number of numbers= 11C3
number of ways 12 can be picked up among 11 numbers= 1C1 = 1
number of ways 15 can be picked up among 11 numbers= 1C1 = 1
number of ways the other slot can be filled = 9C1
total probability = number picked up by John / total list
= (1*1*9C1) / 11C3
What I did on the Test -
Prob of choosing 12 or 15 = 1/11
Prob of choosing the other one of 12 or 15 = 1/10 (because we've already chosen 12)
Prob of choosing a 3rd number = 1
Total probability = (1/11 * 1/10 * 1) * 3! = 3/55
I multiplied by 3! because the 3 numbers can be selected in an unarranged order.
Is the method of solving the question correct?