# 4 cards drawn from deck of 52, what is the probability of exatly one ace?

Update:

I am sorry, make that five cards.

Relevance

Total ways to draw 5 cards = 52!/(47!5!)

Total combinations that include exactly 1 ace:

(4!/(3!1!))*(48!/(44!4!)

So ((4!/(3!1!))*(48!/(44!4!))/(52!/(47!5!)) =

= 4*48!*47!*5!/(44!*4!*52!) =

= 47*46*45*120/(6*49*50*51*52) =

BTW, the other answer you got had the right idea, but forgot to mutiply by 5, since the lone ace could be any one of the 5 cards.

Also, his calculation should be:

5*(1/13*48/51*47/50*46/49*45/48)

• There are 4 Ace cards in deck of 52, hence 48 non-Ace cards in the deck.

You are going to draw 5 cards in total but only 1 being an Ace. Hence here's the number of choices for each of these 5 cards:

Card1: 4 (being an ace)

Card2: 48 (being the 1st non-ace)

Card3: 47 (being the 2nd non-ace)

Card4: 46 (being the 3rd non-ace)

Card5: 45 (being the 4th non-ace)

Mathematically,

No of ways of getting exactly 1 Ace in 5 cards from a 52-cards deck

= (4C1)*(48C4) = 778320

Total number of ways of getting 5 any cards

= (52C5) = 2598960

Probability of getting exactly 1 Ace in 5 cards from a 52-cards deck

= (No of ways of getting exactly 1 Ace in 5 cards from a 52-cards deck) / (Total number of ways of getting 5 any cards)

= 778320 / 2598960

= 0.29947363560808938960199464401145

• Anonymous

the probability that u draw an ace is 4/52 ,for 5 cards drawn

maybe the first one will be an ace OR the second one OR the third....

So Probability= 4/52 +4/52+.....=20/52=0.3846

• All of these answers on here are wrong...You have to assume random sampling in all drawings which mean you have to put the card back you just drew...So, this one is easy.. and I have taught statistics so trust me..

1/52 + 1/52 + 1/52 + 1/52 + 1/52 = 5/52 or .0961 or 9.61%

• Assuming card is replaced B4 drawing other

(4C1)* ((4/52) ^1) * ( (1-4/52) ^3 ) =0.242

Repeated trial

Am i right??

Tell me

Thanks

• You have to draw one ace (1/13) and four "not aces" (12/13 each). In probability, AND means to multiply.

1/13*12/13*12/13*12/13*12/13

=20,736/371,293

=0.0558 or 5.58%