Solving a Combination Problem - Help Appreciated

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In summary, a combination problem is a type of mathematical problem where the order of elements does not matter. To solve it, you need to determine the number of elements and their size, and then use a formula to calculate the number of combinations. The main difference between combinations and permutations is that permutations consider the order of elements. Combination problems have real-life applications in fields such as computer science, statistics, genetics, and probability. An example of a combination problem is selecting toppings for a pizza from a menu.
  • #1
fffbone
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Can anyone explain to me why k!/(k!*(k-k)!)+(k+1)!/(k!*(k+1-k)!)+(k+2)!/(k!*(k+2-k)!)+...+(n-1)!/(k!*(n-1-k)!)=n!/((k+1)!*(n-k-1)!) please. Thanks a lot!
 
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  • #2
Look at the case where n = k+1... then the case where n = k+2...
 
  • #3
logarithm problem help

can you help me with the four following problems by showing me the right procedures of doing it even though it's so troublesome? thanks a lot and i would happily accept any recommended good sites from you guys for this topic.

1)4(2^2x)=8(2^x)-4
2)8(2^2x)-10(2^2x)+2
3)3*2^2x-18(2^x)+24=0
4)9^x-4(3^x)+3=0
 
  • #4
1)4(2^2x)=8(2^x)-4
2)8(2^2x)-10(2^2x)+2
3)3*2^2x-18(2^x)+24=0
4)9^x-4(3^x)+3=0


1) Substitute 2^x with t and the solve the quadratic equation

2) Substitute 2^x with t and then solve the quadratic equation

3) Substitute 2^x with t and the solve the quadratic equation

4) Substitute 3^x with t and the solve the quadratic equation
 
  • #5
Hurkyl,

Sorry, but I didn't quite get where you are going with n=k+1, etc. Could you please explain in more detail?
 
  • #6
How about this:

Assume that [tex]n-k > 1[/tex] and simplify:
[tex]\frac{n!}{(k+1)!(n-k-1)!}-\frac{(n-1)!}{(k+1)!((n-1)-k-1)!}[/tex]

Then compare it to the terms in your series.
 
  • #7
Now I see, thanks.
 
  • #8
I have just one more question:

Why does n!/(0!*(n-0)!)+n!/(1!*(n-1)!)+...+n!/(n!*(n-n)!)=2^n ?
 
  • #9
Use the binomial theorem on [itex](1+1)^n[/itex].
 

1. What is a combination problem?

A combination problem is a type of mathematical problem in which the order of the elements does not matter in the final solution. This means that the same set of elements can be arranged in different ways, resulting in multiple possible combinations.

2. How do you solve a combination problem?

To solve a combination problem, you need to identify the total number of elements and the size of each combination. Then, you can use the formula nCr = n! / (r! * (n-r)!) to calculate the number of combinations. Finally, you can list out all the possible combinations or use other techniques such as tree diagrams or the fundamental counting principle to find the solution.

3. What is the difference between a combination and a permutation?

A combination is a selection of elements where the order does not matter, while a permutation is a selection of elements where the order does matter. In other words, for a combination problem, "ABC" is considered the same as "BAC" or "CAB", while for a permutation problem, "ABC" is different from "BAC" or "CAB".

4. What are some real-life applications of combination problems?

Combination problems can be found in various fields such as computer science, statistics, genetics, and probability. Some real-life applications include creating passwords, scheduling tasks, arranging genetic traits, and predicting outcomes of experiments or events.

5. Can you give an example of a combination problem?

One example of a combination problem is selecting a pizza with three toppings out of a menu of 10 toppings. In this case, the order of the toppings does not matter, and the number of possible combinations is 120 (10C3 = 10! / (3! * (10-3)!)). The combinations could be "pepperoni, mushrooms, olives", "sausage, onions, bell peppers", or "bacon, pineapple, jalapenos", among others.

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