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Example 1
Which value of $m$ satiffies the equation $10! \cdot m = 12!$?
- $11$
- $12$
- $\dfrac{6}{5}$
- $10$
- $132$
Solution
- Divide both sides of the given equation by $10!$ to obtain $m$
$m=\dfrac{12!}{10!}$
- We now need to simplify $\dfrac{12!}{10!}$.
Note that $12!=12 \cdot 11 \cdot 10 \cdot 9...3 \cdot 2 \cdot 1$
$= 12\cdot 11 \cdot 10!=132 \cdot 10!$
- Hence
$m=\dfrac{12!}{10!}=\dfrac{132 \cdot 10!}{10!}=132$
Answer E
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