Question

In how many ways can a set of two positive integers less than 100 be chosen?

Answer 1

In how many ways can a set of two positive integers less than 100 be chosen?

**Solution:**

We have 99 integer and must choose set of two. Number of ways is:

$$C_{99}^2 = \frac{99!}{97! \cdot 2!} = \frac{99 \cdot 98}{2} = 99 \cdot 49 = 4851$$

**Answer:**

Number of ways is 4851.