Question

Determine the total number of five-card hands that can be drawn from a deck of 52 cards.

Answer 1

This is a permutations problem. Do you see that if I draw one card there are 52 possibilities?

Answer 2

ok

Answer 3

So, after I draw the first card, how many possibilities are left for the second card?

Answer 4

47

Answer 5

I took 1 card from 52, how many are left? Why 47?

Answer 6

53

Answer 7

Not 53!
51

Answer 8

51

Answer 9

Have you ever played cards?

Answer 10

no

Answer 11

Suppose I give you 5 letters, abcde OK?

Answer 12

Now, I ask you to pick one. How many possible?

Answer 13

5

Answer 14

If we have n objects (cards, letters or whatever) for the first choice there are
n possible
for the second choice there are
n-1 possible
and so on

Answer 15

Back to the cards, for 52 cards, for the first choice there are
52 possible
for the second choice there are
51 possible
for the third choice there are
50 possible
get the pattern

Answer 16

It's hard if you don't know about cards. So think of the 26 letters of the alphabet, upper and lower case is 52.
You draw one, how many left to choose from?

Answer 17

51

Answer 18

52

Answer 19

OK. So in your problem wie have
52 x 51
go ahead..

Answer 20

2652

Answer 21

Is that what 52 x 51 x 50 x 49 x 48 equals?

Answer 22

no

Answer 23

Do you see why that is the answer?

Answer 24

311875200

Answer 25

so it is 2652

Answer 26

no i think it is 2,598,960

Answer 27

>>> 52 * 51 * 50 * 49 * 48
311875200

Answer 28

That's Python. I never calculate by hand if I can help it.

Answer 29

If there are 52 possible choices of card, and we choose 5 of these
The total number of possibilities is

\[^{52}C_5=\frac{52!}{5!(52-5)!}=\frac{52!}{5!47!}=\frac{52\times51\times50\times49\times48}{5\times4\times3\times2\times1}=\frac{311875200}{120}=\]

their are 52! possible ways to draw all the cards
the cards that have not been drawn are (52-5)!

we divide by the number of choices because this is a combination problem not a permutation problem ~ the order does not matter

Answer 30

Yep, order doesn't matter. My mistake.