We want to find the probability that the first cards selected from a stack of 8 are 5 and 6. To do so, we will use the theoretical probability and compare the number of favorable outcomes to the number of possible outcomes.
P=Favorable Outcomes/Possible Outcomes
We start by finding the number of possible outcomes. We are interested in choosing 2 cards from the stack of 8 cards. Therefore, we look for the number of combinations in which we can choose 2 cards of out 8. The order in which we choose the cards is not important since we are considering them as a pair. Let's recall the combination formula.
_nC_r = n!/r! (n-r)!
This is the formula for the number of combinations of n objects taken r at a time, for 0 ≤ r ≤ n. In our case the stack contains 8 cards, so n= 8. Out of these we choose 2 cards, so r = 2. Let's substitute these values into the formula and evaluate the number of possible combinations.
The number of possible outcomes, of pairs of cards we can draw from the 8 in the stack, is 28. Next, we will look for the number of favorable outcomes, when the pair of selected cards are 5 and 6. Note that there is only one pair of cards with these numbers. Therefore, the number of favorable outcomes is 1. We have enough information to calculate the desired probability.
P=Favorable Outcomes/Possible Outcomes [0.9em]
⇕
P=1/28
The probability that the first cards selected are 5 and 6 is equal to 128.
