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(a) (10 pts) Show that the following equality holds: n +1 + 2 Hint: If you proceed by induction, you might want to use Theorem 1.8.2. If you search for a combinatorial proof, consider the set X - (i,j, k): 0 S i,j< k< n) (b) (10 pts) Prove the following formula: Hint: As above, if you proceed by induction, you might want to use Theorem 1.8.2. If you want a combinatorial proof, you might want to consider the set X = {(i, j, k, l): 0 i,j, k < 1 n)Therom 1.8.2

n choose k = (n choose n-k)

n choose k = (n-1 choose K) + (n-1 choose K-1)

2n = summation of (n choose i )

please use the induction method

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