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 you can write this as a decimal as well if you want to. This is also 0.5. 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.

21. Combinatorics and Probability

Factorials

Precalculus

21. Combinatorics and 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 14\frac1441.

Identify the factorials and fractions involved. Factorials are denoted by '!', and they represent the product of all positive integers up to that number.

Simplify the expression by canceling out common terms. For example, \frac{12}{4!} can be simplified by calculating 4! (which is 4 * 3 * 2 * 1) and then dividing 12 by this result.

After simplifying the fractions and factorials, evaluate the remaining arithmetic operations.

Finally, ensure that all calculations are correct and that the expression is fully simplified to match the given correct answer format.