Answer:
A. The total number of three-card hands (permutations) that can be made with two aces is 576
B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288
C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130
Step-by-step explanation:
A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:
total number of three-card hands (permutations) that can be made with two aces=4*3*52
total number of three-card hands (permutations) that can be made with two aces=576.
B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:
actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48
4C2=4!/2!2!
C2=6
Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288
C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130
