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.

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.