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binomial(4 - 3,3) * binomial(x,y) = binomial(11,- 1)

how to solve it? please give answer in easy way​


Sagot :

Answer:

To solve this equation, we can start by using the fact that:

$\binom{4-3}{3} = \binom{1}{3} = 0$

since there are no ways to choose 3 items from a set of 1 item.

So, the equation becomes:

$0 \times \binom{x}{y} = \binom{11}{-1}$

Now, we know that:

$\binom{11}{-1} = 0$

since there are no ways to choose -1 items from a set of 11 items.

Therefore, the equation is simply:

$0 = 0$

Which is true for any values of x and y!

So, the solution is:

$x \in \mathbb{R}, y \in \mathbb{R}$

In other words, the equation is true for any real values of x and y.

I hope this helps! Let me know if you have any further questions.

Step-by-step explanation:

Let's break it down step by step:

1. Evaluate the first binomial coefficient:

- binomial(4-3, 3) = binomial(1, 3) = 0 (since there's only 1 way to choose 3 items from a set of 1 item, which is none)

2. Multiply the first coefficient by the second binomial coefficient:

- 0 × binomial(x, y) = 0 (since anything multiplied by 0 is 0)

3. Equate the result to the third binomial coefficient:

- 0 = binomial(11, -1)

4. Since binomial(11, -1) is 0 (there's no way to choose -1 items from a set of 11 items), the equation is true!

So, the solution is:

x and y can be any real numbers!

The equation is essentially 0 = 0, which is always true, regardless of the values of x and y.