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

= 3/55

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?

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