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Homework answers / question archive / 2 questions of Combinatorics 1) Let m, n E Z with 0 < m < 7/

2 questions of Combinatorics 1) Let m, n E Z with 0 < m < 7/

Math

2 questions of Combinatorics

1) Let m, n E Z with 0 < m < 7/. Give a combinatorial proof of the equality 
nx—.—nt in n  n 9 /\ m i 1-t — i) = 7) 1—m1 • i=0 
No algebraic manipulations are allowed; you must give combinatorial interpretations of both sides in the way that they are written. 

Q4 (10 points) 
Let n E N. Use lattice paths to give a combinatorial proof of the identity 
(2n \ k n) 1 n-1 1 (2n - 2k - 1\ n - k ) . (21C (2n) n+1 n 4-.0 k 1 k k ) k=0 + 
 

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