Question

Can someone please teach me this in an easier, less difficult way. PLEASE

Answer 1

Answer:

$36$

Step-by-step explanation:

The expression $_nC_k$ is used to denote the number of ways you can choose $k$ things from a set of $n$ things. It is equal to:

$_nC_k=\binom{n}{k}=\frac{n!}{k!(n-k)!}$

In this case, $n=9$ and $k=2$, so:

$\implies \frac{9!}{2!(9-2)!}=\frac{9!}{2!7!}=\boxed{36}$

You can also think of it like this:

$_9C_2$ is saying 9 choose 2. We are choosing 2 things from a set of 9 things, where order doesn't matter. For the first thing we choose, there are 9 options. Then 8 options, 7, and so on. Since we're only choosing two things, there are $9\cdot 8=72$ permutations. However, the order of which we choose each thing does not affect what we've chosen overall (e.g. If we're choosing two donut flavors original and strawberry, it doesn't matter which flavor I choose first, because I'm still getting the same two flavors). Therefore, we must divide this by the number of ways we can arrange two distinct values, which is $2!$. Our answer is thus $\frac{72}{2!}=\frac{72}{2}=\boxed{36}$

Answer 2

Answer:  36

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Explanation:

We have 9*8 = 72 different permutations. This is if we used the nPr formula with n = 9 and r = 2.

Notice the countdown from 9 to 8. This is because we don't reuse the same element twice.

Since order doesn't matter with nCr, we will divide by 2. This is because something like AB is the same as BA. So we go from 72 to 72/2 = 36

The value 36 is found in Pascal's Triangle in the row that has 1,9,... at the start of it. Start at the left hand side and count exactly 3 spaces to the right, and you should land on 36.