Evaluate the expression. 12 4 ! \frac{12}{4!} 4 ! 12

this problem, we're asked to evaluate the expression and the expression we're given is 12 over four factorial. Now there are a couple of different ways that you could choose to do this. For example, if you already know what four factorial is off the top of your head or if you have a calculator that you know how to type factorials into, but I'm gonna go ahead and expand this fully by hand so that you can see what I'm doing step by step. So I'm gonna keep that numerator the same just as 12 because there's nothing to expand there, but then in the denominator I'm going to expand four factorial out into four times three times two times one. Now I want to go ahead and fully multiply this and then of course my numerator stays the same as 12 and then if I multiply this out four times three times two times one this is going to give me 24. Now that I'm here and I don't have any factorials left in this expression I can just simplify it. So I know that 12 over left in this expression, I can just simplify it. So I know that 12 over 24, 12 is one half of 24, so this is actually one half as my fraction. Now you can write this as a decimal as well if you want to. This is also 0.5, but this is our final answer that 12 over four factorial is equal to one half. Thanks for watching and I'll see you in the next one.

14. Sequences & Series

Review of Factorials

Business Calculus

14. Sequences & Series

Review of Factorials

Struggling with Business Calculus?

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Multiple Choice

Evaluate the expression.
$\frac{12}{4!}$

$\frac14$

$\frac12$

$2$

$3$

Verified step by step guidance

Step 1: Understand the problem. The given expression involves factorials and fractions. Factorials are denoted by '!' and represent the product of all positive integers up to a given number. For example, 4! = 4 × 3 × 2 × 1 = 24.

Step 2: Simplify the factorials in the numerator and denominator. For example, if the numerator contains 124! and the denominator contains 4!, calculate these factorials or cancel terms where possible.

Step 3: Simplify the fractions. For example, if you have $ \frac{12}{4!} $, substitute the value of 4! (which is 24) and simplify the fraction $ \frac{12}{24} $.

Step 4: Combine like terms and simplify the entire expression. Ensure that any common terms in the numerator and denominator are canceled out to simplify the fraction further.

Step 5: Verify the final simplified result matches one of the provided answer choices. Ensure all calculations are accurate and consistent with the rules of arithmetic and factorials.