The Fallen Hearts

Probability Level 3

When Agnishom asked the prettiest girl in his class to go on a date with him, she pulled out a standard deck of 52 cards.

She said, "You have to choose 2 cards from this pack without replacement. If both the cards belong to the heart suit, we are on."

As she started shuffling the deck, unknown to either of them, 3 cards inadvertently fell out of the pack at random. In effect the deck was consisting of 49 cards when Agnishom chose his two cards.

Given this scenario, the probability that Agnishom goes on the date i.e. that he draws two hearts without replacement can be expressed as ab\dfrac{a}{b} where aa and bb are co-prime positive integers.

Find the value of a+ba+b.


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