Inclusion-Exclusion.

We do a little more counting.

If you are going to use an ad-blocker, considering using brave and tipping me BAT!

Books I like:

Abstract Algebra:

Differential Forms:

Number Theory:

Analysis:

Calculus:

My Filming Equipment:

[MichaelPennMath]

I uploaded this in the correct order for my course, but just realized it has been unlisted... It's probably time to make it public.

[trueriver]

Another way to calculate the number of subsets is to notice that each element can be present or absent: ie for each potential element there are two possibilities: hence the figure of 2^5 is obvs.

This is a better way to calculate the number of possible subsets. However the method demonstrated here is more powerful because it covers non-exhaustive subsets.

[kevinmartin]

...with the understanding that the Ace can be either high or low on a straight...

[barfyman]

I know that the straight or flush 5-card hands example didn't specify "poker" hands (though you used poker terms straight and flush and did assume Ace can be high or low for the straight, a poker thing), but if you took that interpretation then you would have to again subtract the intersection of A and B because a straight/royal flush is technically neither a straight nor a flush in poker (just like a full house is neither a pair nor a three of a kind even though it contains both).

[michalbotor]

Here's a cool, school-level inclusion-exclusion math problem that i've recently done with my pupil:
"""
In a class of 30 students, 14 are fond of computer science, 10 are fond of chemistry, and 17 are fond of biology, moreover 6 are fond of both biology and computer science, 5 are fond of both biology and chemistry, 11 are fond of computer science but not of chemistry, and 1 is fond of all three of them. Deduce how many students are fond of chemistry only, and how many students are not fond of any one of these subjects.
(Hint: Use Venn diagrams)
"""

[headlibrarian]

When are n and k not integers (or infinity)? Referring to a 5.5 element subset of a 7.3 element list doesn't seem to make sense.

[michaelempeigne]

How to find the lcm of three numbers ?

[RandomBurfness]

God this result is so stupid because there's no real easy way to write out the generalised version for n sets without using dots.

[tomkerruish]

Partway through, I started hearing the voice of Count Von Count a.k.a. The Count.
Five, five, five beautiful one-element subsets! Ah, ah, ah!

[sohamgupta]

Sir I have my INMO (INDIAN NATIONAL MATHEMATICS OLYMPIAD) ON 7 MARCH 2021. SOME TIPS!!