Lesson: Introduction to Combinations

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Dear Brent
I solved the "Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits" question in the following way:

1L 2D
The letter can be chosen out in 26 ways
The digits in 10 x 9 (since the two must be distinct)
And the letter can take one of 3 places within the code.

Therefore, it can be achieved in 26 x 10 x 9 x 3 ways.
(I know the math turns out to be the same, but is the approach wrong? )
gmat-admin's picture

Question link: https://gmatclub.com/forum/will-must-choose-a-3-character-computer-passw...

That's a perfectly valid approach - great work!

Can you pls help me understand my query marked in ALL CAPS:

S is a set of points in the plane (IT DOES NOT MENTION IF THE POINTS ARE COLLINEAR OR DISPERSED). How many distinct triangles can be drawn that have three of the points in S as vertices?

(1) The number of distinct points in S is 5. - SO WHY IS (1) NOT SUFFICIENT ON ITS OWN?

(2) No three of the points in S are collinear.
gmat-admin's picture

Question link: https://gmatclub.com/forum/s-is-a-set-of-points-in-the-plane-how-many-di...

If it isn't stated whether the points are collinear or dispersed, then we can't make any conclusion about their location.

So, when statement 1 tells us that there are 5 points, we have no idea whether the points are collinear or dispersed. Let's examine two possible cases.

Case a - All 5 points are collinear. In this case, we cannot create ANY triangles

Case b - The 5 points are dispersed (no 3 points are collinear). In this case, we can create 10 triangles, since any 3 selected points will create a triangle. 5C3 = 10

Does that help?

How do we identify if the question is counting question or combination question?
gmat-admin's picture

I'm not sure what you mean. Combination questions are a type of counting question. So, if a question is a combination question, then it is also a counting question.

If you're looking for guidance regarding when we need to use combinations and when we need to use a different approach, I cover that in the following video: https://www.gmatprepnow.com/module/gmat-counting/video/788

I've also written 3 articles on that topic:

Article #1: https://www.gmatprepnow.com/articles/combinations-and-non-combinations-%...

Article #2: https://www.gmatprepnow.com/articles/combinations-and-non-combinations-%...

Article #3: https://www.gmatprepnow.com/articles/does-order-matter-combinations-and-...

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