Suppose the first tyre chosen is the rank 3. Then the number of ways ofOriginally Posted bymika

choosing the remaining tyres so that they are all of greater rank is

(as there are five tyres of lower rank than 3):

but the rank three tyre could have been the 1st, 2nd, 3rd or 4th tyre

drawn so there are four times as manny cases like this, and as we are interested

only in combinations we must divide through by the number of permutations

of four objects.

So there are:

different combinations with highest rank tyre being 3.

To find the probability of this occuring we need to divide through by

the number of combinations of tyres which is:

So the required probability is: