How many clubs are in a deck of 52 cards

Asked by admin @ in Mathematics viewed by 294 People

You find a deck of cards and know that the deck has too many clubs and spades in it. The deck has 59 cards.

If you were to draw two cards without replacement, the probability of drawing a diamond and a club is
117
1711
. How many extra spades are in the deck?

Answered by admin @


(13/59)(c/58)=117/1711

13c/3422=117/1711

13c=234

c=18

So there are 18 clubs instead of 13 meaning that there is an extra 5 clubs in the deck.

Since there were 59 cards, there was 7 extra cards in all.  The 7 extra minus the 5 extra clubs leaves 2 extra spaces.

So there were two extra spades in the deck.



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