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Question

Cards are drawn one by one without replacement from a well shuffled pack of 52 cards. Then, the probability that a face card (jack, queen or king) will appear for the first time on the third card is equal to

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Solution

Total No of ways of choosing three cards from the deck = 52C3

As the face card is taken 1st time in three takes, the first 2 takes cannot be face cards.\
So, No of possibilities for 1st 2 takes = 5212C2= 40C2
and as the third take is a face card,
No of possibility for all takes = 40C2×12C1×2

Probability=No of favourable possibilitiesTotal no of ways=40C2× 12C152C3.2=7217×5=7285


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