Use the definition of binomial coefficients to show that each of the following facts is true.
1. [n;n]=1 for any whole number n=>1
2. [n;n-1]=n for any whole number n=>1
3. [n;k]=[n;n-k] for any n and k with k=
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1. [n;n]=1 for any whole number n=>1
2. [n;n-1]=n for any whole number n=>1
3. [n;k]=[n;n-k] for any n and k with k=
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By definition, [n;r] = n!/(r!(n-r)!) with 0! defined as 1.
1. = n!/(n!0!)=n!/n!=1
2 = n!/((n-1)!(1!) since n-(n-1)=n-n+1=1
and n!=n(n-1)! so answer = 1
3) [n;k]=n!/(k!(n-k)!)=n!/((n-k)!k!)=[n;(n-… from definition
1. = n!/(n!0!)=n!/n!=1
2 = n!/((n-1)!(1!) since n-(n-1)=n-n+1=1
and n!=n(n-1)! so answer = 1
3) [n;k]=n!/(k!(n-k)!)=n!/((n-k)!k!)=[n;(n-… from definition
1
keywords: coefficients,Binomial,Binomial coefficients