Chant6j

Answered

2022-07-02

How many ways can you pick exactly the same 4 people from a group of 20

The question is what is the probability that Barbara, Carl, Georg, and Henrietta are randomly chosen from a set of twenty clients for a four-person group date if all possible choices are equally likely?

I know the formula is P = Favorable outcomes / possible outcomes. For whatever reason I am not sure how to get the numerator. The possible outcomes is $(}\genfrac{}{}{0ex}{}{20}{4}{\textstyle )$, but the numerator is alluding me. It is not a multiplication rule because it doesn't allow for repeating, it can't be a permutation because order doesn't matter, leaving a combination I think. but then I did $(}\genfrac{}{}{0ex}{}{20}{4}{\textstyle )$.

I got $\frac{116280}{4845}$, which is a number larger than 1.

What method am I missing? How do I get the number of ways I can exactly pick the Barbara, Carl, Georg, and Henrietta?

The question is what is the probability that Barbara, Carl, Georg, and Henrietta are randomly chosen from a set of twenty clients for a four-person group date if all possible choices are equally likely?

I know the formula is P = Favorable outcomes / possible outcomes. For whatever reason I am not sure how to get the numerator. The possible outcomes is $(}\genfrac{}{}{0ex}{}{20}{4}{\textstyle )$, but the numerator is alluding me. It is not a multiplication rule because it doesn't allow for repeating, it can't be a permutation because order doesn't matter, leaving a combination I think. but then I did $(}\genfrac{}{}{0ex}{}{20}{4}{\textstyle )$.

I got $\frac{116280}{4845}$, which is a number larger than 1.

What method am I missing? How do I get the number of ways I can exactly pick the Barbara, Carl, Georg, and Henrietta?

Answer & Explanation

Oliver Shepherd

Expert

2022-07-03Added 24 answers

Step 1

Let us do it by using combinations: There are 4845 of picking 4 people from 20 (order doesn't matter). Out of those 4845, there is only one possibility of picking Barbara, Carl, Georg and Henrietta.

Step 2

Therefore, there is a $\frac{1}{4845}$ chance that those 4 will be picked.

Let us do it by using combinations: There are 4845 of picking 4 people from 20 (order doesn't matter). Out of those 4845, there is only one possibility of picking Barbara, Carl, Georg and Henrietta.

Step 2

Therefore, there is a $\frac{1}{4845}$ chance that those 4 will be picked.

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