Bridge game distribution of cards

63. you are dealt a 13-card bridge hand from a 52-card bridge deck.

b. what is the probability you will be dealt at least 2 hearts?

so i think i figured this out... just not sure if i'm missing more to the equation...

N=52 (population)

n=13(sample size)

x=2(number of successes)

number of failures = n-x

= 13-2

= 11

P(at least 2 hearts) = 13 39

2 11

---------

52

13

= 78(1,675,986,051) / 6.53 x 10^11

= 1.307 x 10^11 / 6.35 x 10^11

= 0.20583

therefore, the probability you will receive at least 2 hearts is 0.20583 or 20.583% chance.

c. What is the probability that you will receive 5 hears, 4 clubs, 2 diamonds and 1 spade?

so i already calculated out for 5 hearts in part a. and came to 0.12472

N=52 still?

n=8 (we already took 5 cards)

x= 4

number of failures = n-x

= 8-4

= 6

P(4 clubs) = 8 39

4 6

---------

52

8

= 70(3,262,623)/752,538,150

= 228,383,610/752,538,150

= 0.30345

now N=52

n = 4

x = 2

number of failures = n-x

= 4-2

= 2

P(2 diamonds) = 4 39

2 2

---------

52

4

= 6(741)/270,725

= 4,446/ 270,725

= 0.01642

N=52

n=2

x=1

number of failures=n-x

= 2-1

= 1

P(1 club) = 2 39

1 1

---------

52

2

= 2(39)/1,326

= 78/1,326

= 0.05882

then to find the total probability it would be;

Pt = P(5 hearts) + P(4 spades) + P(2 diamonds) + P(1 club)

= 0.12472 + 0.30345 + 0.01642 + 0.05882

= 0.50341

Therefore the probability that you will be dealt 5 hearts, 4 spades, 2 diamonds and 1 club is 0.50341 or 50.341%?

Again with this question i just want to make sure that i've got this figured out the right way...