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Please help me on MC-II A Combinatoric homework questions.

 
 
YangYoyo的头像
Please help me on MC-II A Combinatoric homework questions.
YangYoyo 发表于 2019年01月27日 Sunday 11:00
 

Hello people!

When I was doing homework problems 7.24 and 7.25, I didn't really understand the problems. Is it okay if someone explains it a little bit more? Thank you!

Have a good day!

Yoyo =^w^=


 
ReynosoDavid的头像
Re: Please help me on MC-II A Combinatoric homework questions.
ReynosoDavid 发表于 2019年01月28日 Monday 11:51
 

On 24 we want to associate to each number in the set $A$ a subset of $B$. Note $A$ has exactly $2^n$ elements, and since $B$ has $n$ elements, there are also $2^n$ subsets of $B$ (for each element in $B$ it is either on the subset or it is not). The hint says "think of the elements of A written in binary", so for example to take $5\in A$, since $5 = 2^2 + 1 = 101_2$ and you can associate the subset of $B$ $\{1, 3\}$, since it has a $1$ in the first and third positions (from right to left) when written in binary. Can you do this with each of the numbers of $A$?

On 25 we want to show that counting the number of ways to put $n$ identical balls into $k$ different boxes is the same as counting the number of non-negative solutions to $a_1 + a_2 + \cdots a_k = n$. Can you think of a rule that assigns a way to arrange the balls with a solution to the equation (and vice versa)?

YangYoyo的头像
Re: Please help me on MC-II A Combinatoric homework questions.
YangYoyo 发表于 2019年01月28日 Monday 18:13
 

Thank you Mr. David! Have a good day!

-Yoyo