How many ways can you pick exactly the same 4 people from a group of 20The 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 ( 20 4 ) , 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 ( 20 4 ) .I got 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?

Question

How many ways can you pick exactly the same 4 people from a group of 20The 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                     (                    20              4                            )            , but the numerator is alluding me. It is not a multiplication rule because it doesn&#039;t allow for repeating, it can&#039;t be a permutation because order doesn&#039;t matter, leaving a combination I think. but then I did                     (                    20      4                      )            .I got       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?

Oliver Shepherd · Accepted Answer

Step 1Let us do it by using combinations: There are 4845 of picking 4 people from 20 (order doesn&#039;t matter). Out of those 4845, there is only one possibility of picking Barbara, Carl, Georg and Henrietta.Step 2Therefore, there is a       1    4845   chance that those 4 will be picked.