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Find the value of the following: (12!10!)/(11!11!) If your answer is not an integer, write it as an exact fraction. square

Pergunta

Find the value of the following:
(12!10!)/(11!11!)
If your answer is not an integer, write it as an exact fraction.
square

Find the value of the following: (12!10!)/(11!11!) If your answer is not an integer, write it as an exact fraction. square

Solução

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Ana CéliaEspecialista · Tutor por 3 anos

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To find the value of the expression \frac{12! \cdot 10!}{11! \cdot 11!}, we can simplify it by canceling out common factors in the numerator and denominator.

First, let's write out the factorials explicitly:

12! = 12 \times 11!


So, the expression becomes:

\frac{12! \cdot 10!}{11! \cdot 11!} = \frac{12 \times 11! \cdot 10!}{11! \cdot 11!}


Next, we can cancel out the 11! terms in the numerator and denominator:

\frac{12 \times 11! \cdot 10!}{11! \cdot 11!} = \frac{12 \times 10!}{11!} = \frac{12 \times 10!}{11 \times 10!} = \frac{12}{11}


Thus, the value of the expression is:

\boxed{\frac{12}{11}}
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