Respuesta :
Vanessa can take 20 different groups of 3 books
What is combination?
"It is a way of selecting items from a collection where the order of selection does not matter."
Formula of combination:
For selecting 'r' items from a collection of 'n' items,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
For given question,
Vanessa has 6 unique books, but only 3 fit in her bag.
We need to find the number of different groups of 3 books she can take.
Here, n = 6 and r = 3
Using the formula of combination,
[tex]\Rightarrow ^6C_3=\frac{6!}{3!(6-3)!}\\\\\Rightarrow ^6C_3=\frac{6\times 5\times 4\times 3!}{3!\times3!}\\\\ \Rightarrow ^6C_3=\frac{120}{3\times 2\times 1} \\\\ \Rightarrow ^6C_2=20[/tex]
Therefore, Vanessa can take 20 different groups of 3 books.
Learn more about combination here:
https://brainly.com/question/13387529
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