Is 106 = 9Cx correct for this combination problem?

  • MHB
  • Thread starter mathdad
  • Start date
In summary, the conversation discussed a question about combinations and whether the given formula was correct. It was determined that the formula needed additional parentheses to be accurate. However, it was also pointed out that there may not be a natural number solution to the problem. The original source of the problem was not remembered but it was acknowledged that some math posts on Facebook may be inaccurate.
  • #1
mathdad
1,283
1
I found an interesting question online. It involves combination.

106 = 9Cx

I know the combination formula but can someone set it up for me?

Here is my endeavor:

106 = 9!/x!(9 - x)!

Is this correct?
 
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  • #2
RTCNTC said:
106 = 9Cx
You sure that should be 106?

(9)C(x), x = 1 to 9:
9,36,84,126,126,84,36,9,1
 
Last edited:
  • #3
6C2 + 7C4 + 8C5 = 9Cx
 
  • #4
RTCNTC said:
6C2 + 7C4 + 8C5 = 9Cx
Says who?
 
  • #5
Wilmer said:
Says who?

I found this question online not from a textbook.
 
  • #6
I gave you the possible solutions: none equals 106.

Can you give us the url of the site?
 
  • #7
RTCNTC said:
Here is my endeavor:
106 = 9!/x!(9 - x)!
The right side should be 9! / (x!(9 - x))
Do you see why the extra set of brackets is required?

Once more: there is NO SOLUTION = 106
 
  • #8
RTCNTC said:
106 = 9!/x!(9 - x)!

You need appropriate parentheses. The above should be

9!/(x!(9 - x)!)
 
  • #9
6C2 + 7C4 + 8C5 = 9Cx

6C2 = 15

7C4 = 35

8C5 = 56

15 + 35 + 56 = 9Cx

50 + 56 = 9Cx

106 = 9Cx

Do you see where 106 comes from?
 
  • #10
RTCNTC said:
6C2 + 7C4 + 8C5 = 9Cx
6C2 = 15
7C4 = 35
8C5 = 56
15 + 35 + 56 = 9Cx
50 + 56 = 9Cx
106 = 9Cx
Do you see where 106 comes from?
Doesn't matter where it comes from.
Look buddy, give us the link to where you found
this problem...else you're on your own...
 
  • #11
I found this problem in a facebook math group but there are so many that I truly don't recall the name of the group. This question is not so important. Thanks anyway.
 
  • #12
Like Wilmer, I found that there is no natural number solution to that problem. W|A was able to return 2 numeric approximations, but with a problem like this, we expect natural numbers. Seeing the original problem would have helped to clear up the issue. :)
 
  • #13
Sorry if I sounded exasperated Mr.RTCNTC.

I've seen quite a few "Facebook math posts" that are inaccurate...
 
  • #14
Can we just move on?
 

FAQ: Is 106 = 9Cx correct for this combination problem?

1) What is the purpose of finding x in combination problems?

The purpose of finding x in combination problems is to determine the value of an unknown variable in a given equation or problem. This is often necessary in order to solve the problem or to find a specific solution.

2) How do you approach finding x in combination problems?

The best approach to finding x in combination problems is to first identify all of the known values and variables in the problem. Then, use mathematical operations such as addition, subtraction, multiplication, and division to isolate x on one side of the equation. Finally, solve for x by plugging in the known values and simplifying the equation.

3) What are some common strategies for solving combination problems?

Some common strategies for solving combination problems include using the fundamental counting principle, using permutations and combinations, and using tree diagrams. It is also important to carefully read and understand the problem and to use logic and critical thinking skills to determine the best approach.

4) Are there any tips for finding x in combination problems?

There are a few helpful tips for finding x in combination problems. One tip is to always double check your work and make sure that you have correctly applied the mathematical operations. Another tip is to use units and labels to help keep track of the different variables and their values. Additionally, it can be helpful to break down the problem into smaller, more manageable steps.

5) What are some real-world applications of finding x in combination problems?

Finding x in combination problems has many real-world applications in areas such as science, engineering, finance, and statistics. For example, scientists may need to find the value of an unknown variable in an equation to determine the concentration of a chemical in a solution. Engineers may use combination problems to determine the optimal design for a structure or machine. In finance, finding x can help with calculating interest or determining the return on an investment. In statistics, finding x can help with analyzing and interpreting data.

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