Respuesta :

CarlosRCR
Combinations can be written as something called "binomial coefficient", in this case, you are looking for '5 combine 3', which is written as the binomial coefficient "5 in top of 3" it looks like a fraction but without the horizontal line separating the two numbers.

A binomial coefficient "n in top of k" (or n combine k) can be also written as:

[tex] \frac{n!}{k!(n-k)!} [/tex]

So 5 combine 3 is equal to:

[tex] \frac{5!}{3!2!} = \frac{5*4*3*2*1}{(3*2*1)(2*1)}= \frac{5*4}{2}=10 [/tex]

There exist 10 possible combinations.

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