# You order fifteen burritos to go from a Mexican restaurant, eight with hot peppers and seven without. However, the restaurant forgot to label them. If you pick five burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

All have hot peppers.

15C5=15!/10!5!=3003 for the total
8C5=8!/3!5!=1209600 for hot
Is this correct so far?

## Well, let's taco about it. Your calculation for the total number of combinations is correct, so good job on that! However, your calculation for the number of combinations with all hot peppers seems a bit off.

You see, if we have 8 burritos with hot peppers and we want to pick 5, we actually need to use 8C5, not 8C5. The formula for combinations is nCr, where n represents the total number of items and r represents the number of items we want to choose.

So, the correct calculation for the number of combinations with all hot peppers is 8C5 = 8!/5!(8-5)! = 56.

Now, to find the probability of this event, we divide the number of desired outcomes (56) by the total number of outcomes (3003). So, the probability is 56/3003, which simplifies to approximately 0.019, rounded to three decimal places.

So, the probability of picking five burritos at random and all of them having hot peppers is about 0.019. Good luck with your spicy burrito adventure!

## No, your calculations are incorrect. Let's correct them:

The total number of ways to choose 5 burritos out of 15 is given by the combination formula:

nCr = n! / (r!(n-r)!)

15C5 = 15! / (5!(15-5)!)
= 15! / (5!10!)
= (15 * 14 * 13 * 12 * 11) / (5 * 4 * 3 * 2 * 1)
= 3003

So the total number of ways to choose 5 burritos out of the 15 is indeed 3003.

Now, for the number of ways to choose 5 burritos with hot peppers out of the 8 available, we can calculate it:

8C5 = 8! / (5!(8-5)!)
= 8! / (5!3!)
= (8 * 7 * 6) / (3 * 2 * 1)
= 56

Therefore, the number of ways to choose 5 burritos with hot peppers out of the 8 available is 56.

To calculate the probability that all 5 burritos have hot peppers, we divide the number of successful outcomes (5 burritos with hot peppers) by the total number of possible outcomes (choosing 5 burritos out of 15):

P(All have hot peppers) = (number of ways to choose 5 burritos with hot peppers) / (number of ways to choose 5 burritos out of 15)
= 56 / 3003
≈ 0.019 (rounded to three decimal places)

Therefore, the probability that all 5 burritos have hot peppers is approximately 0.019.

## No, your calculations are incorrect.

To calculate the probability of picking five burritos with hot peppers out of the fifteen, we need to determine the total number of possible combinations and the number of combinations that satisfy the event.

First, let's calculate the total number of combinations of picking any five burritos out of fifteen. This can be done using the combination formula:

Total combinations = 15C5 = 15! / (5!(15-5)!) = 3003

Now, let's calculate the number of combinations where all five burritos have hot peppers. Since there are 8 burritos with hot peppers, we need to select all five from that group. This can be calculated as:

Combinations with all hot peppers = 8C5 = 8! / (5!(8-5)!) = 56

Finally, to find the probability, we divide the number of desired combinations by the total number of combinations:

Probability = (Combinations with all hot peppers) / (Total combinations)
= 56 / 3003
≈ 0.018 (rounded to three decimal places)

Therefore, the probability of randomly selecting five burritos with all of them having hot peppers is approximately 0.018.