need the solution

For discussing Olympiad Level Combinatorics problems
kh ibrahim
Posts:17
Joined:Mon May 09, 2016 11:18 am
need the solution

Unread post by kh ibrahim » Sat Jul 08, 2017 7:31 pm

x takes part in three subjects physics, chemistry and mathematics.Each of the subjects is of 100 marks.How many ways can he obtain 200 out of 300?

User avatar
Abdullah Al Tanzim
Posts:24
Joined:Tue Apr 11, 2017 12:03 am
Location:Dhaka, Bangladesh.

Re: need the solution

Unread post by Abdullah Al Tanzim » Sun Jul 30, 2017 11:35 am

I think it is $ \frac {102.101}{ 2} $. Notice if you get o in physics then you will have only one way to get 200 marks in the three subjects.if you get 1 in physics then you will have 2 ways and for 2 you will have 3 ways and it will go on for o to 100 ..It forms a series that
$ 1+2+3+.............+101$ and the sum of the series is $ \frac {102.101}{2} $... :)
Everybody is a genius.... But if you judge a fish by its ability to climb a tree, it will spend its whole life believing that it is stupid - Albert Einstein

Golam Musabbir Joy
Posts:11
Joined:Tue Jun 16, 2015 5:11 am
Location:Barisal, Bangladesh

Re: need the solution

Unread post by Golam Musabbir Joy » Sat May 19, 2018 8:04 pm

We can solve this problem in this way too.
We will count in how many ways x can miss $100$ marks out of $300$.
let $p$ be the missed marks in physics, $c$ be the missed marks in chemistry and $m$ be the missed marks in mathematics. so we have to find in how many ways $p+c+m=100$ can be possible where $0\leq p,c,m \leq 100$ and the answer is $102\choose 2$ that is $5151$

NABILA
Posts:35
Joined:Sat Dec 15, 2018 5:19 pm
Location:Munshigonj, Dhaka

Re: need the solution

Unread post by NABILA » Mon Jan 14, 2019 9:24 pm

I didn't understood the last line.
Wãlkîñg, lõvǐñg, $mīlïñg @nd lìvíñg thě Lîfè

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: need the solution

Unread post by samiul_samin » Wed Jan 16, 2019 9:29 pm

NABILA wrote:
Mon Jan 14, 2019 9:24 pm
I didn't understood the last line.
That is a combinatorial notation.
It means in how many ways you can choos $2$ people from $101$ people.
Example:
Ways of choosing $4$ people from $5$ people=$5C4$
:arrow: $(5×4×3×2×1)/(1×2×3×4)$

NABILA
Posts:35
Joined:Sat Dec 15, 2018 5:19 pm
Location:Munshigonj, Dhaka

Re: need the solution

Unread post by NABILA » Thu Jan 17, 2019 2:54 pm

Hmm. Understood.
Wãlkîñg, lõvǐñg, $mīlïñg @nd lìvíñg thě Lîfè

Post Reply