Q&A #3398

Teachers' Lounge Discussion: Permutations and counting arrangements

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From: Loyd

To: Teacher2Teacher Public Discussion
Date: 2003041410:49:46
Subject: Re: HELP

On 2000101815:38:16, Andrea wrote: >I am a grade 13 or OAC student in Canada. I am currently taking a >Finite class the is learning, at the moment, Combinatorics. I am >having an extreamly difficult time with the concept of this chapter >and was wondering if someone would be able to help. Here is an >example question that has me stuck... > > > Prove: > > 1 over (a-1)!n! + 1 over a!(n-1)! = a+n over a!n! > Rewrite the problem as: 1 + 1 a+n ----------- ---------- = ------ (a-1)!n! a!(n-1)! a!n! Multiply 1st term on left by 1 in the form of: a!(n-1)! -------- a!(n-1)! Multiply 2nd term on left by 1 in the form of (a-1)!n! ----------- (a-1)!n! When you do that you will have a!(n-1)! + (a-1)!n! ----------- ---------------- a!(n-1)!(a-1)!n! a!(n-1)!(a-1)!n! Which reduces to: a + n ----- ----------- a!n! a!n! That should do it. Notice that a!/(a-1)!=a. That is the key to solving this problem. The rest is just solving equations by finding the LCD. Pretty tough problem for a 13 year old.

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