a deck of cards haa 52 cards. in it has 4 of {aces,2,4,3,4,5,6,7,8,9,10,queens,kings,and jacks well you know} what is the probability of getting 4 aces at a time? express your answers as a common fraction.
ps. the answers 4/52 or simplfied is not the answer!!!
Thanks your help is greatly appreciated gracias!!!
Pr(4 aces)=4/42*3/41*2/40*1/39=4!38!/42!
Thanks for your help but when you put the fraction /42 or is it suppose to be 52 gracias
To find the probability of getting 4 aces at a time from a standard deck of 52 cards, we can use the concept of combinations.
First, let's determine the total number of ways to choose any 4 cards from the deck of 52. This can be represented as C(52, 4), which means "52 choose 4" and can be calculated using the formula:
C(n, r) = n! / (r!(n-r)!)
Where "!" denotes factorial, and n and r represent the total number of objects and the number of objects to be chosen, respectively.
Plugging in the values, we have:
C(52, 4) = 52! / (4!(52-4)!)
= 52! / (4!48!)
= (52*51*50*49) / (4*3*2*1)
= 270,725
This means that there are 270,725 different combinations of choosing any 4 cards from a standard deck of 52.
Next, let's determine the number of ways to choose exactly 4 aces from the deck. Since there are only 4 aces in the deck, we can write this as C(4, 4), which is equivalent to choosing all 4 aces at once.
C(4, 4) = 4! / (4!(4-4)!)
= 1
Therefore, there is only 1 combination of choosing exactly 4 aces from the deck.
Finally, we can calculate the probability by dividing the number of successful outcomes (choosing 4 aces) by the total number of outcomes (choosing any 4 cards):
Probability = successful outcomes / total outcomes
= 1 / 270,725
So, the probability of getting 4 aces at a time from a standard deck of 52 cards is:
1 / 270,725
This is the simplified fraction representing the probability.