Respuesta :
If a high school student decides to apply four of six famous colleges, then the four colleges can be selected in as many as 15 different combinations.
As per question statement, a high school student decides to apply four of six famous colleges.
We are required to calculate the number of combinations in which the four colleges can be selected.
To solve this question, we need to know the formula of Combination which goes as [tex](nCr)=\frac{n!}{r!(n-r)!}[/tex]
, i.e., we are to select a set or "r" from a set of "n".
Here, we have to select a combination of 4 from a set of 6.
Therefore applying (nCr) formula with (n = 6) and (r = 4), we get,
[tex](6C4)=\frac{6!}{4!(6-4)!} =\frac{6!}{4!2!}=\frac{4!*5*6}{4!*2}=\frac{5*6}{2}=(5*3)=15[/tex].
- Combinations: In mathematics, a combination is a method of selecting items from a particular set, where the order of selection does not matter, i.e., if we have a set of three P, Q and R, then in how many ways we can select two numbers from each set, can be easily defined by combination.
To learn more about combinations, click on the link below.
brainly.com/question/8561440
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