Mathematics, 14.08.2020 08:01 hardwick744

Evaluate plz plz plz help me i am soo confused

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Answer from: juniorgutierrez997

Hey there! I'm happy to help!

QUESTION 100

Here, we are looking for the number of permutations. A permutation is the number of possible arrangements you can make from a given set of things (order matters). If you have 6 kids standing in alphabetical order in line, that is one permutation. If you do reverse alphabetical order, that is a different permutation.

We are asked to find the number of permutations using the given format:

$_{n}P_{r}\\$

This is simply a representation of what we want to find. The P means we are looking for the number of permutations. The n is the total number of objects in the set (for example, if there were 26 kids we could choose from to make this 6 person line, n would be 26). The r is the number of things chosen from the set (in our line example, the r would be six because we are choosing 6 kids).

The formula for finding the number of permutations is $\frac{n!}{(n-r)!}$ . The ! is factorial, it means you multiply that number by every integer counting backwards towards 1. 6! is 6×5×4×3×2×1. There is an option to do this on your calculator, though.

Let's solve this problem.

$_{5}P_{4}=\frac{5!}{(5-4)!}= \frac{120}{1} =120$

This means that there are 120 permutations.

QUESTION 101

Now we have a C. This is similar to permutations but with combinations order does not matter. With our line example, having the same six kids in alphabetical order is a different permutation than having it in backwards alphabetical order. With combinations, if you have those specific six kids, it is just one combination; the order does not matter.

The formula for combinations is $\frac {n!}{r!(n-r)!}$ . Let's plug in our numbers and solve for this.