The tarot minor arcana deck has 56 cards in four suits (swords, batons, coins, and cups),...

The tarot minor arcana deck has 56 cards in four suits (swords, batons, coins, and cups), each having 10 numbered cards and 4 court cards (king, queen, knight, and page). A “spread” is a draw of 9 cards. What is the probability of getting a spread of all court cards?

Expert Solution

To get the probability of getting a spread of all court cards we will divide the no of ways to get a spread of all court cards by the total possible ways of getting a spread.

Now total possible ways of getting a spread is the way of choosing 9 cards from all 56 cards. So total number of possible spread is .

There are total 4*4=16 court cards. So now to get a spread of all court cards we must choose 9 cards from those total 16 court cards and must not choose any other card. But the ways of choosing 9 cards from 16 court cards is . So total number of possible spread having all court cards is .

So the required probability is

That is approximately equal to 1.51*10^-6.

[Hope this helps. Ask in the comments if you still have any doubt or wants any more clarification. I will be glad to help. Thanks.]

Colby Messinger answered 2 years ago

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