- #1
NotaMathPerson
- 83
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Find n if P(n, 3) = 6 C(n, 5).
My attempt
$\frac{n!}{(n-3)!}=6\frac{n!}{(n-5)5!}$
I don't know how to proceed
My attempt
$\frac{n!}{(n-3)!}=6\frac{n!}{(n-5)5!}$
I don't know how to proceed
NotaMathPerson said:Find n if P(n, 3) = 6 C(n, 5).
My attempt
$\frac{n!}{(n-3)!}=6\frac{n!}{(n-5)5!}$
I don't know how to proceed
NotaMathPerson said:Find n if P(n, 3) = 6 C(n, 5).
My attempt
$\frac{n!}{(n-3)!}=6\frac{n!}{(n-5)5!}$
I don't know how to proceed
As http://mathhelpboards.com/members/mrtwhs/ pointed out there is a typo on the first line. It is fixed on the second line.soroban said:
[tex]\begin{array}{ccc}\text{We have:} & \dfrac{n!}{(n-3)!}\;=\; 6\dfrac{n!}{(n-5)5!}\\ \\
\text{Cross-multiply:} & 5!\,n!\,(n-5)! \;=\;6\,n!\,(n-3)! \\ \\
\text{Divide by 6n!:} & 20(n-5)! \;=\;(n-3)! \\ \\
\text{We have:} & 20(n-5)! \;=\;(n-3)(n-4)(n-5)! \\ \\
\text{Divide by }(n-5)! & 20 \;=\;(n-3)(n-4) \\ \\
\text{Simplify:} & n^2 - 7n - 8 \;=\;0 \\ \\
\text{Factor:} & (n+1)(n-8) \;=\;0 \\ \\
\text{Solve:} & n=\cancel{-1}.\;8
\end{array}[/tex]
Permutation is used when the order of the elements matters, while combination is used when the order does not matter. For example, if you are choosing a president, vice president, and secretary from a group of 10 people, you would use permutation because the order of the chosen individuals matters. However, if you are choosing a committee of 3 people from a group of 10, you would use combination because the order of the chosen individuals does not matter.
The formula for permutation is nPr = n! / (n-r)!, where n is the total number of elements and r is the number of elements being chosen. The formula for combination is nCr = n! / (r!(n-r)!), where n is the total number of elements and r is the number of elements being chosen.
Factorial notation is used in permutation and combination equations when there is a need to find the number of possible arrangements or combinations of a certain number of elements. It is represented by an exclamation mark after the number, such as 5!.
Yes, permutation and combination equations are commonly used in real-life situations such as in probability and statistics, genetics, and computer science. They are used to calculate the number of possible outcomes or arrangements in a given scenario.
Some common mistakes to avoid when solving permutation and combination equations include: