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?

Suppose there are x number of clubs in the pack 

P( draw a diamond) = 13 / 59 
P( draw a club) = x / 58 

so P( diamond then a club) = 13x / (58*59)  = 13x / 3422

so we have the equattion
 117 / 1711 = 13x / 3422
 234 / 3422 = 13x / 3422

therefore   x = 234 / 13 =  18 clubs :-

that is 5 more clubs than  in a normal pack 
So the number of extra spades  = 59 - 52 - 5 =  2

The decimal expansion would be .27 repeated