**Big Thank you**
Dear Soroban,

Thanks very much for your detailed solution but I have

some hiccup which I hope you can shed some light to me.

Thanks very much

Kingman

In your solution you wrote;

The first draw can be any of the 15 numbers: .15/15=1

I believe you are referring to the sum of the 15 outcomes

eg.(1,other,1), (2,other,2),(3,other,3),( 4,other,4)

.............(15,other,15) from which the sum of the probability equals to 15*(1/15*14/15*1/15) Is this what you mean?

Also I cannot see how the outcome of the numerator of

you conditional probability equation (1)

.
can be a subset of the denominator when the outcome of the denominator has 3 element ,whereas the outcome of the numerator has 4,5,6 and 7 elements

Eg. The outcomes of the denominator looks like

.(1,other,1), (2,other,2),(3,other,3),( 4,other,4)

.............(15,other,15)

Whereas the numerator looks like (1,other,1,1)…. (15, others,15,15)

And (1, others,1, other , 1), ……..(15, others,15, other , 15)

And (1, others,1, other ,other, 1), ……..(15, others,15, other , other,15)

And (1, others,1, other ,other, other 1), ……..(15, others,15, other , other, other15)