of 12 possible books, you plan to take 4 with you on vacation. how many different collections of 4 books can…

Explanation:

Step1: Identify the combination formula

The formula for combinations is (C(n,r)=\frac{n!}{r!(n - r)!}), where (n) is the total number of items, and (r) is the number of items to be chosen. Here, (n = 12) and (r=4).

Step2: Calculate factorial values

(n!=12! = 12\times11\times10\times9\times8!), (r!=4! = 4\times3\times2\times1), and ((n - r)!=(12 - 4)!=8!) Substitute into the formula: (C(12,4)=\frac{12!}{4!(12 - 4)!}=\frac{12\times11\times10\times9\times8!}{4\times3\times2\times1\times8!})

Step3: Simplify the expression

Cancel out the (8!) terms. Then calculate (\frac{12\times11\times10\times9}{4\times3\times2\times1}) (12\div4 = 3), (10\div2=5) The expression becomes (3\times11\times5\times9=1485)

Answer:

(1485)