From a deck of 52 cards, how many different 5-card hands can be formed in each case?

Question

From a deck of 52 cards, how many different 5-card hands can be formed in each case?
a) with exactly 3 spades
b) with at least 3 spades
c) with at most 3 spades

Answer 1

Dragonsong is close, A & B are right:
a) 13 x 12 x 11 x 39 x 38 = 2,543,112

b) 13 x12 x11 x 49 x 48 = 4,036,032

But for C first pick 2 non-spades, then for the last three cards pick from all of the remaining cards.

C = 39 x 38 x 50 x 49 x 48 = 174,283,200

Answer 2

With 52 cards, there are 13 spades and 39 other cards

a) 13 x 12 x 11 x 39 x 38 = 2,543,112

b) 13 x12 x11 x 49 x 48 = 4,036,032

c) 13 x 12 x 11 x 39 x 38 = 2,549,112

Answer 3

a. 13 x 12 x 11 x 39 x 38 = 2543112
b. (13 x 12 x 11 x 39 x 38) + (13 x 12 x 11 x 10 x 39) + (13 x 12 x 11 x 10 x 9) = 3366792
c. (39P5) + (13 x 39 x 38 x 37 x 36) + (13 x 12 x 39 x 38 x 37) + (13 x 12 x 11 x 39 x 38) = 105850368
hope i'm right.

Answer 4

concerning question 2 - despite the count variety is whilst it is your turn to play dictates what you do. So while you're sitting interior the 5th field and four gamers on your authentic take taking part in cards then which will replace the count variety. counting on the type of folk on the table the count variety can upward thrust or drop very at as quickly as. If the working count variety is plus 8 till now the hand is dealt, the three gamers each and each catching intense taking part in cards drops the working count variety down by skill of 6 factors very right now.