16. Simplify 6p2
30
15
12
720
17. Simplify 8c5
6,720
336
56
10
Okay, so the formula for Permutations is n!/(n-r)! and the formula for Combinations is
n!/r!(n-r)! however I don't quite know how to figure either of these out. I'm sort of blanking here! Please help.
BTW, Ms. Sue, if "this is not your area," then don't comment on this. That simple.
16. Well, let's have some fun with permutations! Now, imagine you're throwing a party and you have 6 people to invite. You want to know how many different ways you can choose 2 out of those 6 fun-loving individuals.
So, 6p2 means we're doing a permutation with 6 items and we want to choose 2 of them. Using the formula n!/(n-r)!, we plug in the numbers, giving us 6!/(6-2)!.
Now, if I do some calculations in my clown brain, that means 6! is 6 × 5 × 4 × 3 × 2 × 1, and (6-2)! is 4 × 3 × 2 × 1.
If we simplify, we get 720/(24), which gives us 30! Ta-da! The answer is 30.
17. Now, regarding combinations! This time, let's imagine you're a cashier with 8 different flavors of ice cream. You want to know how many different combinations there are if a customer can choose 5 flavors.
Using the combination formula n!/r!(n-r)!, we substitute the numbers. It becomes 8!/5!(8-5)!.
Once again, let my clown brain do some math magic. We have 8! which is 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, and 5! which is 5 × 4 × 3 × 2 × 1, and finally (8-5)! which is 3 × 2 × 1.
After simplifying, we get 56. That's the number of combinations, my friend!
So, there you have it! Permutations and combinations made easy and humorous just for you. Now, it's time for me to do some juggling with numbers, or maybe just clown around. Enjoy your day!
No problem! I can help you understand permutations and combinations and how to calculate them.
Permutations refer to the arrangement of objects in a particular order, while combinations refer to the selection of objects without considering the order. To calculate permutations, you use the formula n!/(n-r)!, where n represents the total number of objects and r represents the number of objects being arranged.
On the other hand, combinations are calculated using the formula n!/r!(n-r)!, where n represents the total number of objects and r represents the number of objects being selected.
Now let's simplify the given examples:
16. Simplify 6p2:
To calculate permutations, we use the formula 6!/(6-2)!.
So, it becomes 6!/4!, which simplifies to (6x5x4x3x2x1)/(4x3x2x1).
Canceling out the common factors, we get (6x5) = 30.
Therefore, the answer is 30.
17. Simplify 8c5:
To calculate combinations, we use the formula 8!/(5!(8-5)!).
So, it becomes 8!/(5!x3!), which simplifies to (8x7x6x5x4x3x2x1)/(5x4x3x2x1x3x2x1).
Canceling out the common factors, we get (8x7x6)/(3x2x1).
Therefore, the answer is 56.
I hope this helps clarify how to calculate permutations and combinations! Let me know if you have any further questions.
No problem! I can help you understand how to calculate permutations and combinations.
Permutations are used when the order is important, while combinations are used when the order doesn't matter.
Let's start with permutations. The formula for permutations is n! / (n - r)!, where n represents the total number of items you have to choose from, and r represents the number of items you are selecting.
To simplify the expression 6P2, we substitute the values into the formula. In this case, n = 6 and r = 2:
6P2 = 6! / (6 - 2)!
= 6! / 4!
Now, to calculate the factorials. The factorial of a number is the product of all positive integers less than or equal to that number.
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
4! = 4 x 3 x 2 x 1 = 24
Substituting these values back into the expression:
6P2 = 720 / 24
= 30
So, the simplified value of 6P2 is 30.
Now, let's move on to combinations. The formula for combinations is n! / (r! * (n - r)!).
To simplify the expression 8C5, we again substitute the values into the formula. In this case, n = 8 and r = 5:
8C5 = 8! / (5! * (8 - 5)!)
= 8! / (5! * 3!)
Calculating the factorials:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320
5! = 5 x 4 x 3 x 2 x 1 = 120
3! = 3 x 2 x 1 = 6
Substituting these values back into the expression:
8C5 = 40,320 / (120 * 6)
= 40,320 / 720
= 56
Therefore, the simplified value of 8C5 is 56.
I hope this explanation helps! If you have any further questions, feel free to ask.