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.