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 4 factorial. Now there are a couple of different ways that you could choose to do this, for example, if you already know what 4 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 4 factorial out into 4 times 3 times 2 times 1. 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 3 times 2 times 1, 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 24 12 is 1 half of 24 so this is actually 1 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 4 factorial is equal to 1 half. Thanks for watching, and I'll see you in the next one.

10. Combinatorics & Probability

Factorials

College Algebra

10. Combinatorics & Probability

Factorials

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Multiple Choice

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

$\frac14$

$\frac12$

$2$

$3$

Verified step by step guidance

First, understand the expression: $ 124! \frac{12}{4!} 4! 12 $. This involves factorials and division.

Factorials are denoted by $!$ and represent the product of all positive integers up to that number. For example, $4! = 4 \times 3 \times 2 \times 1 = 24$.

Simplify the expression by calculating $4!$ and substituting it into the expression. This will help in simplifying the division part $\frac{12}{4!}$.

Next, perform the division $\frac{12}{24}$ which simplifies to $\frac{1}{2}$.

Finally, multiply the simplified result by the remaining terms in the expression to evaluate the entire expression.