If I put 4 of the 10 presents under the Christmas tree, how many combinations of presents can be picked, where 2 of the presents are from me?

To find the number of combinations of presents that can be picked, where 2 of them are from you, we can use the concept of combinations.

In this case, you want to select 2 presents from the 4 presents you've placed under the Christmas tree. The remaining 6 presents can be selected by anyone else.

So, the number of combinations can be calculated using the formula for combinations, which is:

C(n, k) = n! / (k! * (n-k)!)

Where C(n, k) denotes the number of combinations of n items taken k at a time, and n! represents the factorial of n.

Applying this formula to your scenario, you would have:

C(4, 2) = 4! / (2! * (4-2)!)

Calculating the factorial expressions:

C(4, 2) = 4! / (2! * 2!)

Simplifying the factorials:

C(4, 2) = (4 * 3 * 2 * 1) / (2 * 1 * 2 * 1)

Cancelling out the common terms:

C(4, 2) = (4 * 3) / (2 * 1)

So, the number of combinations of presents that can be picked, where 2 presents are from you, is 6.

Therefore, there are 6 different combinations of presents that can be picked in this scenario.