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 4 Number of partitions of $n$ with $k$ parts equals the number of partitions of $n + \binom k {2}$ 2 Formula for $\sum _{i=1}^n (n+1-i) (n-i)$ 1 Lottery: Finding the probability of winning respective prizes 0 Number of permutations for n elements with different probabilities 0 Probability of having exactly 1 pair from drawing 5 cards

### Reputation (150)

 +10 Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) +15 Number of permutations for n elements with different probabilities +10 Number of partitions of $n$ with $k$ parts equals the number of partitions of $n + \binom k {2}$ +5 Balls, Bags, Partitions, and Permutations

### Questions (4)

 4 Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) 2 Smallest $n$ for which, we can have $k$ distinct subsets of $[n]$ such that no two of them have empty intersection 2 Count the subsets of [n] whose sum is modulo $2^k$ 1 Balls, Bags, Partitions, and Permutations

### Tags (7)

 5 combinatorics × 8 0 permutations × 2 4 partitions × 2 0 number-theory 2 summation 0 card-games 1 probability × 3

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 Mathematics 150 rep 6 Stack Overflow 1 rep Programmers 1 rep Computer Science 1 rep MathOverflow 1 rep