Evaluate six factorial minus four factorial minus two factorial.
The word “factorial” in mathematics means the product of an integer and all the positive integers below it. This means that in this question, six factorial means six multiplied by five multiplied by four multiplied by three multiplied by two multiplied by one. In the same way, four factorial involves multiplying the integers four, three, two, and one. Finally, two factorial is equal to two multiplied by one.
Let’s start with this bottom one. Two multiplied by one is equal to two. Four multiplied by three is equal to 12. Multiplying this by two gives us 24 and 24 multiplied by one is equal to 24. We can do the same for six factorial. Multiply six by five, multiply the answer by four, then by three, by two, and by one.
If the integer becomes large, an easier way of doing this is to use the factorial button on our scientific calculator. Pressing the number six, the factorial button, and then equals gives us an answer of 720. We were asked to evaluate six factorial minus four factorial minus two factorial. This is the same as 720 minus 24 minus two. Subtracting 24 from 720 gives us 696. Subtracting another two gives us 694.
Six factorial minus four factorial minus two factorial is equal to 694.