# Combinations Problem: Solving k Value in Homework Equation

• temaire
In summary, the conversation is about a problem and solution for a math question. The person is questioning how the value of k is 3 and is unable to ask the teacher before a test. The solution involves expanding and finding the coefficient of x^11 and solving for k using the equation 3k-10=11.
temaire

## Homework Statement

http://img234.imageshack.us/img234/8519/combgf7.png​
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## Homework Equations

$${t}_k_+_1=_n{C}_kx^n^-^ky^k$$

## The Attempt at a Solution

The picture I have shown contains the problem and the teacher's solution. However, I was wondering how the $$k$$ value is 3. And no, I can't ask the teacher; my test is tomorrow.

Last edited by a moderator:
This is how I would do it

$$(x^2+\frac{1}{x})^{10}=[\frac{1}{x}(x^3+ 1)]^{10}$$

$$=\frac{1}{x^{10}}(x^3+1)^{10}$$

and you want the coefficient of $x^11$

so if you expand you will get

$$=\frac{1}{x^{10}}(...+^{10}C_k(1)^{10-k}(x^3)^k+...)$$

You need to find k and you want the power of x to be 11

so that 3k-10=11

See it?

rock.freak667 said:
$$=\frac{1}{x^{10}}(...+^{10}C_k(1)^{10-k}(x^3)^k+...)$$

You need to find k and you want the power of x to be 11

so that 3k-10=11

For your expansion, isn't the 1 supposed to be where the $$x^3$$ is? Because 1 is the y value, while $$x^3$$ is the x value.

Also, k doesn't equal 3 in $$3k-10=11$$

## What is a "Combinations Problem" in a homework equation?

A combinations problem in a homework equation involves finding the number of ways to select or arrange a specific number of items from a larger set, without repetition and without regard to order.

## How do you solve for the "k" value in a combinations problem?

The "k" value in a combinations problem represents the number of items being selected or arranged. To solve for this value, you can use the formula nCk = n! / (k!(n-k)!), where n is the total number of items in the set.

## What is the difference between combinations and permutations?

In combinations, the order of the selected items does not matter, while in permutations, the order does matter. Additionally, combinations do not allow for repetition of items, while permutations do.

## How can I apply combinations problems in real life?

Combinations problems can be used in a variety of real-life situations, such as determining the number of possible outcomes in a lottery, the number of ways to select a committee from a group of people, or the number of possible combinations of toppings on a pizza.

## Can combinations problems be solved using a calculator?

Yes, most scientific or graphing calculators have a combinations function (usually denoted as "nCr") that can be used to solve combinations problems. You can also use the factorial function (usually denoted as "!") to manually solve for combinations.

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