On her coffee table, Sharon has a pile of 7 magazines. She plans to get through 2 of them over the weekend. How many sequences of 2 magazines are possible?

The problem can be solved using the concept of combinations in mathematics.

A combination is a selection of items where order does not matter. In this case, Sharon can choose 2 magazines out of 7 in any order.

The formula for combinations is:

C(n, r) = n! / [r!(n-r)!]

where:

• n is the total number of items,
• r is the number of items to choose,
• "!" denotes factorial, which is the product of all positive integers up to that number.

Substituting the given values into the formula:

C(7, 2) = 7! / [2!(7-2)!]

This simplifies to:

C(7, 2) = (7654321) / [(21)(54321)]

After canceling out the common factors, we get:

C(7, 2) = (76) / (21) = 21

So, there are 21 different sequences of 2 magazines that Sharon can choose from.