Problem: It’s My Lucky Year

A marked lotto ticket.
A marked lotto ticket.

Here’s a chance to flex those combinatorics muscles. A lottery is drawn by selecting five integers at random from 1 to 69 inclusive, without replacement. The result is reported in increasing order.

What is the probability that the pair “20 22” occurs consecutively on the winning ticket? To be clear, “05 10 19 20 22” counts, but “05 10 20 21 22” does not.

Once you’ve got that worked out, find a lucky year; one for which the first two significant figures of the probability, expressed as a percentage, are identical to the year modulo 100. For example, 2029 is a near miss with its 0.2892% chance of occurring. No rounding!

Can we find all the lucky years?

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