Math CentralQuandaries & Queries


Question from Rajshri, a student:

A class has 100 students with roll numbers 1 to 100. Six students are selected, one after another, at random to form a team. Find the probability that

(A)the roll numbers of first three students selected are in ascending order and

(B)the roll numbers of the last four students selected are in descending order.

Hint: IF the two events "A" and "B" were independent this problems would be rather easy. But they aren't: if (A) is true then the third student's number is likely to be high, making (B) more likely.

How can you rephrase this in terms of events that are independent?

Specifically, which of the six students must have the highest roll number? And once this is given, what other easy and independent conditions give the desired event?

Good Hunting!

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