Multiplying and Dividing Factorials

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Math › Multiplying and Dividing Factorials

Questions 1 - 7

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Explanation

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

Simplify and solve $\frac{100!}{97!}$ .

$7.5*10^{15}$

Explanation

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, .

Rather than do all of the math involved for , notice that $\frac{100!}{97!}$ is the same as $\frac{100*99*98*97!}{97!}$

From here, the 's cancel out, leaving us with .

Simplify $\frac{ 8!}{6!}$ .

Explanation

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

Which of the following is equivalent to $6!\times4!$ ?

$30\times(4!)^2$

$(6!)^{2}-4!$

None of the other answers are correct.

Explanation

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

$6\times5!$

$\frac{6\times(5!)^2}{4!}$

$5\times6!$

$30\times5!$

$6\times5^{2}\times4!$

Explanation

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Solve the following expression.

$\frac{10!}{8!}$

Explanation

$\frac{10!}{8!}=\frac{10*9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{10*9*8!}{8!}=10*9=90$

Solve:

$\frac{10!}{7!}$

Explanation

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

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