Of 10 possible books, you plan to take 7 with you on vacation. How many different collections of 7 books can you take?
You can take different collections of 7 books on vacation with you.
Final Answer: There are \(\boxed{120}\) different collections of 7 books you can take on vacation with you.
Step 1 :This problem is about combinations. We are choosing 7 books out of 10, order does not matter, and we can't choose the same book more than once.
Step 2 :The formula for combinations is: \(C(n, k) = \frac{n!}{k!(n-k)!}\), where n is the total number of items, k is the number of items to choose, and ! denotes factorial.
Step 3 :In this case, n = 10 (the total number of books) and k = 7 (the number of books to choose).
Step 4 :Substituting the values into the formula, we get \(C(10, 7) = \frac{10!}{7!(10-7)!}\)
Step 5 :Solving the above expression, we find that the number of combinations is 120.
Step 6 :Final Answer: There are \(\boxed{120}\) different collections of 7 books you can take on vacation with you.