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](https://static.questionai.br.com/resource%2Fqaiseoimg%2F202501%2Ffind-value-following12101111if-answer-integer-write-tBZoQvmPdP0A.jpg?x-oss-process=image/resize,w_558,h_500/quality,q_35/format,webp)
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
![expert verified](https://mathresource.studyquicks.com/static/image/br/verify.png)
4.3203 Voting
![avatar](https://static.questionai.br.com/resource%2Favatar%2Fbr%2Ffemale%2Fa3460_fd998be68901e40963c6.jpg?x-oss-process=image/format,webp)
Ana CéliaEspecialista · Tutor por 3 anos
Responder
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}}
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}}
Clique para avaliar: