# Can someone explain to me how to do this probablily question (1 Viewer)

Cheers

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#### RossoneriAU

##### Member
Combinations --> There are 52 cards in the deck, and 5 need to be picked out. No. of potential combinations is 52C5 which is 2,598,960. In seeing this, we can figure out that you can get 4 aces in 48 different ways because, assuming you get all 4 aces as your first 4 cards, there are 48 other cards that you can get that fulfil our criteria (4 aces out of 5 cards). Thus, your fraction is number of possible outcomes of you getting 4 aces in 5 cards divided by the total number of outcomes. As said before, there are 48 different ways of getting 4 aces in 5 cards, and there are 2,598,960 possible outcomes

48 / 2,598,960 = 1 / 54145 or in percentage terms, 0.0018469%

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#### cossine

##### New Member
I think this question involves hypergeometric distribution as number cards decease by 1 as each is dealt.

i.e. P(?AAAA) = 48/52 * 4/51 * 3/50 * 2/49 * 1/48

Maybe you could consider the cases: ?AAAA, A?AAA, AA?AA, AAA?A, AAAA? and find the probability that way.

i.e. Find the value of: P(?AAAA) + P(A?AAA) + P(AA?AA) + P(AAA?A) + P(AAAA?)

#### AnnPreston

##### New Member
Oh god, i was learning it at the university and i've forgot already everything... cossine said correctly...

#### Fizsi

##### New Member
5 arrangements of AAAAN. Each one has numerators 4x3x2x1x48. Denominators are 52x51x50x49x48. So 5 x(numerator product) divided by (denominator product) =1/54145

#### RakeshCristoval

##### Member
Combinations --> There are 52 cards in the deck, and 5 need to be picked out. No. of potential combinations is 52C5 which is 2,598,960. In seeing this, we can figure out that you can get 4 aces in 48 different ways because, assuming you get all 4 aces as your first 4 cards, there are 48 other cards that you can get that fulfil our criteria (4 aces out of 5 cards). Thus, your fraction is number of possible outcomes of you getting 4 aces in 5 cards divided by the total number of outcomes. As said before, there are 48 different ways of getting 4 aces in 5 cards, and there are 2,598,960 possible outcomes

48 / 2,598,960 = 1 / 54145 or in percentage terms, 0.0018469%
gotcha cheers mate

#### tickboom

##### New Member
Check out the following video if you would like a step-by-step solution:

#### tito981

##### Member
Oh god, i was learning it at the university and i've forgot already everything... cossine said correctly...
Isn’t this like 2u math?