please help me with this STATISTICS problem... I have no idea what to do with it!?

Question

this is the problem...

>>> In a standard deck of crads there are 52 cards, there are 4 suits for each of the cards 2,3,4,5,6,7,8,9,10,jack,queen,king, and ace.
what is the probability of getting 4 kings and 4 aces when drawing 10 cards????

Answer 1

The answer to your question is
"the number of ways of drawing 4 kings and 4 aces" divided by "the number of ways of drawing 10 cards"

"The number of ways of drawing 4 kings and 4 aces" is the same as "the number of ways of drawing 2 cards from a pack with kings and aces missing (52-8)", which is 44!/(2! * 40!)

"The number of ways of drawing 10 cards from 52" is 52!/(10! * 42!)

The quotient is therefore:
44! * (10! * 42!) / (2! * 40! * 52!) =
(42 * 41 * 44! * 10!) / (2 * 52!) =
(42 * 41 * 10!) / (2 * 52 * 51 * 50 * 49 * 48 * 47 * 46 * 45) =
(6 * 41 * 9 * 3* 4) / (52 * 51 * 47 * 46 * 45) =
(6 * 41) / (26 * 17 * 47 * 23 * 5) =
(3 * 41) / (13 * 17 * 47 * 23 * 5)

Answer 2

Assuming no cards are returned to the deck, and that you want the probability of getting 4 kings and 4 aces in that order:

4/52 * 3/51 * 2/50 * 1/49 * 4/48 * 3/47 * 2/46 * 1/45
=
1.898x10^-11
=
1.898x10^-9 %

(very unlikely)