Math HELP!?

Question

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

a) There are only aces or face cards
b) There are only cards numbered 2,3,4,5,6,7,8,9, and 10
c) There are only clubs.

With some explanation please?

Answer 1

a)
there are a total of 16 cards, so you just combination it.
16!/(11!5!) sorry I don't have a calculator with me
b) so there are 9 * 4 cards, 36 cards, so you just combo 36.
36!/(31!5!) the exclamation is factorial, btw
c) there are 13 cards that are clubs, so you just combo that
13!/(8!5!)

Don't forget the formula for combination n!/((n-b)!b!)
where n is the total possible choices and "b" is the number you need to form (where ABCDE and BCDEA are the same)

Answer 2

When analyzing 5-card hands, order is not important. These are known as combinations, not permutations.

a) Aces or face cards
There are 4-J, 4-Q, 4-K, and 4-A for a total of 16 cards.
When selecting combinations of five cards, the choices are:
(16 x 15 x 14 x 13 x 12) / (1 x 2 x 3 x 4 x 5)
(16! / 11!) / 5! = 4368 combinations

b) 2 thru 10
9 cards x 4 suits = 36 cards
(36! / 31!) / 5! = 376,992 combinations

c) only clubs
There are 13 cards per suit.
(13! / 8!) / 5! = 1287 combinations

Did you notice the shortcut of multiplying the large series of numbers? Most calculators have a FACTORIAL button, n!. By dividing out the extra factorial piece you can quickly get the product of several large values. Just subtract the number of choices you get to make and divide by that factorial value.

Answer 3

a) there are 4 aces and 12 faces card. That make 16 total.
You select 5 out of16.
(16*15*14*13*12) / (5!) = 4368

b) there are 36 number-cards. select 5 out pf 36
(36*35*34*33*32) / (5!) = 376,992

c) there are 13 club cards. Select 5 out of 13
(13*12*11*10*9) / 5! = 1287

Answer 4

ok
5 cards are being picked
a.) since only aces and face card. so there are.. 12 face cards and 4 aces. which means that the total is 16
so.. its 16 ! selection from 5so.. its 16 x15 x14 x13x12
this is because when of the face cards or aces are drawn the overall possbilities of pulling the other face cards and aces are now 15 choices and so on and so forth
b.) since the only cards numberd for 2 3 4 5 6 7 8 9 10
there are.. 4 each?? so its.. 4x9 =36 choices in total?
and its selection from 5 so its 36 x 35 x 34 x 33 x32
c.) there are... 13 clubs.. so.. 13 x 14 x 13 x 12 x11 (5 selections)

Answer 5

a) 16*15*14*13*12 = 524160
b) 36*35*34*33*32 = 45239040
c) 13*12*11*10*9 = 154440