# Lesson: Calculating Combinations

## Comment on Calculating Combinations

### God bless u.you soo good﻿

God bless u.you soo good﻿

Thank you.

### you are great!!! THIS SHORT

you are great!!! THIS SHORT CUT IS IS NOT THOUGHT IN SCHOOLS.

thank you, YOU ARE BEST MATH TEACHER.

-> I HAVE ONE MORE QUESTION -> IF I HAVE DONE A WRONG STEP CALCULATION NPR INSTEAD OF NCR FOR "ORDER DOESNT MATTER" SELECTION QUESTIONS, CAN i STILL GET THE CORRECT ANSWER BY DIVIDING THE OUTCOME WITH 2.

-> IN SHORT WHAT IS MEANT IS => COMBINATION=1/2(OUTCOME OF PERMUTATION) AT LEAST WHEN THERE IS A TOTAL VALUE N A EVEN NUMBER. HOW ABOUT THE APPROACH? ALWAYS DIVIDE OUTCOME BY 2 AND RECHECK WITH ANSWER CHOICES? WILL THIS WORK?
PLEASE RPLY -THANKS AND REGARDS VINEET

### Thanks for the kind words,

Thanks for the kind words, Vineet.

In general, if you accidentally use nPr (instead of nCr), you can find the correct result if you divide your calculation by r!

So, for example, if you accidentally calculate 5P2 (instead of 5C2), you can find the correct result if you divide your calculation by 2!

Does that help?

Cheers,
Brent

ASIDE: I'm not a big fan of permutations as they pertain to GRE counting questions. For more on this, read: https://www.greenlighttestprep.com/articles/combinations-and-non-combina...

### Great tip. This is exact what

Great tip. This is exact what I was looking for. I was spending way too much time on calculations.

### Regarding the pizza problem.

Regarding the pizza problem. How can I tell that it's not a combination with repetition problem? On the mathisfun site, their is an example problem with ice-cream which states: "Let us say there are five flavors of icecream: banana, chocolate, lemon, strawberry and vanilla.

We can have three scoops. How many variations will there be?"

I don't see how the ice cream problem is different from the pizza problem, but it must be.

Oh, I guess it's assumed we can not repeat the pizza topping? So, that would make it a combination without repetition problem?

### Good question!!

Good question!!

In your ice cream example, there's no text that says we can't have 2 or more scoops of the same ice cream.

However, the pizza question uses the term "3-topping pizza," which (for me) suggests the 3 toppings must be different.
For example, if we chose mushrooms, mushrooms, and mushrooms for the pizza, is it still a 3-topping pizza?
That said, I fully recognize that I may have chosen an ambiguous way to phrase the question.
It would probably be better if I had added a proviso that says "the 3 toppings must be different"

Cheers,
Brent

### https://greprepclub.com/forum

https://greprepclub.com/forum/at-flo-s-pancake-house-pancakes-can-be-ordered-with-any-of-5102.html
Since no toppings were repeated, shouldn't the answer be 6x5x4?

### The key here is that the

The key here is that the order in which we select the pancake toppings does not matter.
For example, choosing strawberries, blueberries and whipped cream as pancake toppings is the same as choosing blueberries, whipped cream and strawberries as pancake toppings.
His order and which we select the toppings does not matter, will use combinations.

### Hey, can you help me with the

Hey, can you help me with the answer: How many ways can 4 boys and 3 girls be seated at a round table? I got it as 7! which is not the right answer

### If this were an official GRE

If this were an official GRE question, there would be an extra proviso explaining that arrangements where each person's RELATIVE position is the same are considered identical. Here's what I mean:
Let's say there are 4 people seated at a circular table, and A is seated in the top chair, and in clockwise order, we have B, C and D.
This arrangement is considered the same as one in which B is seated in the top chair, and in clockwise order, we have C, D and A.
In both arrangements, B is to the left of A, C is to the left of B, D is to the left of C, and A is to the left of D. As such, those two arrangements are considered equivalent.

To account for these duplicate arrangements, we have the following general formula:
We can seat n people at a circular table in (n-1)! ways.

So, for this question, we can arrange the 7 people in (7-1)! ways.
(7-1)! = 6! = 720.