Question 1056986
The number of ways that a hand of 5 spades can be drawn is:


C(13, 5) * C(39, 0) = {{{(13!/(5!(13-5)!)) * (39!/(0!(39-0)!))}}} = 1287 * 1 = 1287 ways


The number of ways that ANY 5-card hand can be drawn from a deck of 52 cards is:


C(52, 5) = {{{52! / (5!(52-5)!)}}} = 2598960


The probability is then:


P(5 spades) = {{{1287/2598960}}} = 0.00049520 = <strong>0.0495%</strong>


For the hand with exactly 3 face cards, there are 12 face cards in the deck (3 in each suit),
and 52 - 12 = 40 non-face cards.


The number of ways of drawing a 5-card hand with exactly 3 face cards is equal to 
the number of ways of selecting 3 out of 12 face cards, multiplied by the number of
ways of selecting 2 of the 40 non-face cards:


C(12, 3) * C(40, 2) = {{{(12!/(3!(12-3)!)) * (40!/(2!(40-2)!))}}} = 220 * 780 = 171600


The number of ways of drawing any 5-card hand is still 2598960 (from above)


The probability is then:


P(exactly 3 face cards) = {{{171600/2598960}}} = 0.0660264 = <strong>6.6026%</strong>