## Problem Of The Week 53

**How many ways can a size k + 1 subset with maximum element m + 1 can be created from the given set S={1,2,3,…..,n+1} ?**

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**How many ways can a size k + 1 subset with maximum element m + 1 can be created from the given set S={1,2,3,…..,n+1} ?**

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Written by Implex

October 15, 2008 at 12:43 pm

Posted in Algebra, Problem of the week

Tagged with Algebra, Combinatorics

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Here, the maximum value that m can take is n and same for k.

Tried with examples but m not able to come to a general solution.

When m=k, the no. of ways =1

When m>k, the solution is

(m+1)C{k+1) + mC(k+1) + (m-1)C(k+1)…

A stupid solution I know. Working on generalizing this.

Still in CAT the best way to tackle such questions would be to go for value of n=5/6 and the values of k upto 5 and similarly for m.

milindOctober 20, 2008 at 4:42 pm

its simpler

the highest term can be selected in one way

as it is m+1

now other k terms have to be selected from m values

so mck

outtimedOctober 21, 2008 at 12:36 pm