how to solve this?

For discussing Olympiad Level Combinatorics problems
Badhonholmes
Posts: 7
Joined: Fri Jun 29, 2018 12:02 pm

how to solve this?

Unread post by Badhonholmes » Fri Apr 05, 2019 8:27 pm

in how many ways 10 can be the sum of 4 natural numbers?
10=1+2+3+4
10=1+1+1+7
10=1+1+2+6
10=1+1+3+5
10=1+1+4+4

10=2+2+2+4
10=2+2+3+3
and these permutations add up to 68 how to get other permutations?

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samiul_samin
Posts: 999
Joined: Sat Dec 09, 2017 1:32 pm

Re: how to solve this?

Unread post by samiul_samin » Wed Apr 10, 2019 10:17 am

Formula$\dbinom{n-1}{k-1}$
You can get a link of nice book
Here

Badhonholmes
Posts: 7
Joined: Fri Jun 29, 2018 12:02 pm

Re: how to solve this?

Unread post by Badhonholmes » Wed Apr 10, 2019 9:11 pm

i know the formula. i wanted to count by hands but could not find more than 68

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