Find the value of \(rac{100!}{98! \times 3!}\) Circle your answer. - AQA - A-Level Maths Mechanics - Question 2 - 2019 - Paper 3

To find the value of (\frac{100!}{98! \times 3!}), we can simplify this expression using the property of factorials. Specifically, we know that (100! = 100 \times 99 \times 98!). Thus, the expression can be rewritten as:

$$\frac{100 \times 99 \times 98!}{98! \times 3!}$$

The (98!) cancels out, yielding:

$$\frac{100 \times 99}{3!}$$

Since (3! = 3 \times 2 \times 1 = 6), we can further simplify:

$$\frac{100 \times 99}{6}$$

Calculating this gives:

$$\frac{9900}{6} = 1650$$