Video: Solve a Calculation Involving Factorials

Evaluate 7! + 6! + 5!.


Video Transcript

Evaluate seven factorial plus six factorial plus five factorial.

Let’s firstly consider what the word factorial means in mathematics. The factorial of any integer is the product of that integer and all the positive integers below it. Let’s consider five factorial first. This is equal to five multiplied by four multiplied by three multiplied by two multiplied by one. Five multiplied by four is equal to 20. Multiplying this by three gives us 60. Multiplying 60 by two is 120. And finally, multiplying this by one gives us an answer of 120. Five factorial is equal to 120.

Six factorial is the product of six, five, four, three, two, and one. We already know that five factorial is equal to 120. Multiplying this by six gives us 720, as six multiplied by 12 is 72. We can work out seven factorial using the same method, multiplying our answer for six factorial by seven. Seven multiplied by 720 is 5040. There is a quicker method of doing this: by using the factorial button on the calculator. To work out seven factorial, we would type seven, the factorial button, and then equals. This would give us an answer of 5040.

In this question, we’re asked to evaluate seven factorial plus six factorial plus five factorial. We need to add 5040, 720, and 120. This gives us an answer of 5880. If we didn’t have a calculator, we could do this using the column method. The ones or unit column sum to zero. The tens column sum to eight. The hundreds column sum to eight. And the thousands column sum to five. Seven factorial plus six factorial plus five factorial has a value of 5880.

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