Online Course Discussion Forum

MC-II A Problems

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MC-II A Problems
by Eddy zheng - Saturday, December 22, 2018, 3:58 PM

I am not sure how to start problems 4.25, 4.26, and 4.30.


Picture of Yoyo Yang
Re: MC-II A Problems
by Yoyo Yang - Thursday, January 3, 2019, 7:32 PM
For 30 A, think of the books as balls and the kids as boxes, and then it will be like question 4.5 we did in class. Yeah, I am still working on the rest :) happy new year!
Picture of Derek Wong
Re: MC-II A Problems
by Derek Wong - Sunday, January 6, 2019, 8:10 AM

Hi Eddy! This is Derek :D

So for 4.25, it is similar to problem 4.10 (if y'all got the time to do it in class) If not, you can refer to the textbook (if you have it); it has explanations on the back for problem 4.10.

Anyway, I think the best approach to this one is complementary counting and some PIE. 

Hope this helps!

Picture of David Reynoso
Re: MC-II A Problems
by David Reynoso - Thursday, January 10, 2019, 11:35 AM

For 25, as Derek mentions, it is similar to example 4.10. Consider three sets, where you count the number of ways friend 1, friend 2, and friend 3 get no books. Use them to find the number of ways at least one of the friends gets no books. Then use complementary counting.

For 26, try using complementary counting: how many regions would you have in a Venn diagram with three sets like the one described in the problem? Use this to find the total number of ways you could choose the sets $A$, $B$ and $C$. Then do the same assuming you only have two sets, this should help counting what happens when $A=\varnothing$.

On 30, when asked to do PIE consider sets where one of the friends gets no books (like in 25). To count using cases it might help figuring out first the different ways to add to $5$ using three positive numbers.