## Solution to Puzzle #79: Diwali Special

This was a very nice puzzle and I got many responses, though only one of which was completely correct – from Girish Tutakne. What was commendable was that he sent his answer literally within a few minutes of my posting the puzzle! I also got partially correct answers – my niece Radhika (in class 8) sent the answer to the first two parts, and so did Vaibhav Kalia. Thanks again to Alok Mittal for contributing this puzzle!

Here are the answers and the explanations (copying a god chunk of Girish’s answers):

1. Answer is 1/3…since there are three different numbers, the probability of each of them being the last one is 1/3 and hence the probability that the middle one is the third one is also 1/3.
1. When you select 3 cards from a suit, they will obviously be different cards. So, then this problem boils down to the first one again and prob that 3rd card is between first two is again 1/3
1. This is slightly tricky because there is a chance of repetition. So, our answer is 1/3 of the Prob of drawing 3 distinct cards from the deck.

Prob of drawing 3 distinct cards = (52x48x44)/(52x51x50).

Hence, final answer is (1/3)x (52x48x44)/(52x51x50) = 4576/16575 = 0.276

Hope you enjoyed the puzzle.

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