need the solution

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

need the solution

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?

Abdullah Al Tanzim
Posts: 24
Joined: Tue Apr 11, 2017 12:03 am

Re: need the solution

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

Re: need the solution

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

I didn't understood the last line.