### Questions (11)

 21 Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$ 18 What is the fastest way to multiply two digit numbers? 9 How many ways to divide group of 12 people into 2 groups of 3 people and 3 groups of 2 people? 6 How many ways dividing $n$ balls into $3$ buckets with limitations? 3 Find $\sum\limits_{k=\frac{n+1}{2}}^n{n \choose k}$ closed form

### Reputation (803)

 +40 Combinatorial proof of $\sum\limits_{k=0}^n {n \choose k}3^k=4^n$ +10 How many ways to assemble a team of 5 out of 15 girls and 10 boys with limitations? +50 What is the fastest way to multiply two digit numbers? +10 How to prove that the union of two subspaces must be subsets of each other?

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 0 combinatorics × 5 0 generating-functions 0 linear-algebra × 3 0 matrices 0 binomial-coefficients × 2 0 mental-arithmetic 0 combinatorial-proofs 0 recurrence-relations 0 determinant 0 summation

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 21 Resources/Books for Discrete Mathematics

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