Question

Of 19 possible​ books, you plan to take 6 with you on vacation. How many different collections of 6 books can you​ take?

Answer 1

27,132

Explanation:

Since the order of the books isn't important, we'll use combinations.

`_nC_r=(n!)/(r!(n-r)!)`

where nCr is the number of combinations,

n is the population size,

and r is the sample size.

Here, n = 19 and r = 6.

₁₉C₆ = 19! / (6! (19−6)!)

₁₉C₆ = 19! / (6! × 13!)

₁₉C₆ = 27,132