Hello I am looking for simple help in R Studio here are the questions You collec

Question

Hello I am looking for simple help in R Studio here are the questions You collect 75 mosquitos and find that 8 are infected. How many unique ways could this have happened (i.e., how many different ways can you sample 8 out of 75)? If you were to collect 75 mosquitos, what is the probability that the first eight that were collected were infected, and the remainder where not? Now I know to find probability(like for 8 out of 75) we use dbinom(8,75,prob=0.23) but I am not sure how to find all the possible ways of 8 or just the first 8, etc.

Explanation / Answer

possible ways of 8:

In mathematics, a combination is selection of items from a collection, such that (unlike permutations) the order of selection does not matter.

So, 8 out of 75 = 75C8 = 16871053725

which can be calculated in R by

choose(75,8)

choose(75,8)
[1] 16871053725
>

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