Find the value of 100! 98! × 3! Circle your answer - AQA - A-Level Maths Pure - Question 2 - 2019 - Paper 3

To simplify the expression, we can use the formula for factorials:

rac{100!}{98! imes 3!} = rac{100 imes 99 imes 98!}{98! imes 3!}

Cancelling the $98!$ from the numerator and denominator, we have:

rac{100 imes 99}{3!}

Next, calculate $3!$:

$$3! = 3 imes 2 imes 1 = 6$$

So now we simplify:

rac{100 imes 99}{6}

Calculating the numerator:

$$100 imes 99 = 9900$$

Then divide by 6:

rac{9900}{6} = 1650

Thus, the value of the expression is 1650.