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 Feb 21 answered Number of permutations for n elements with different probabilities Oct 9 comment Number of permutation with non-consecutive blocks Why don't you think along these lines? Compute the number of strings having at least one "BC" as the sub string. Now, subtract it from the total number of strings. It is simple this way. Isn't it? Oct 9 comment Little help with permutations You're right about the number of possible codes. What did you try for second part. Oct 2 comment all possible sequences of positive integers that sum upto N and are strictly increasing @BrianMScott: Thanks, I missed the part that we can use $N$ bricks only and we have to use all the $N$ bricks. Oct 1 comment all possible sequences of positive integers that sum upto N and are strictly increasing @BrianMScott: Did I get the question wrong? Please help. As per the OP description, the number of stairs possible with only two steps = $\binom{N}{2}$ ( choose two numbers, the order is fixed ). But, the number of partitions of $N$ into exactly $2$ distinct parts is $\lfloor \frac{N}{2} \rfloor - 1$. I see that the bijection is possible only when the OPs requested sequence always ends with $N$. Am I right? Please help me understand the bijection, if I'm wrong. Sep 26 comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) Here's one more. $$15873 \times 7 = 111111, 15873 \times 14 = 222222 \cdots$$ Mar 22 awarded Commentator Mar 22 comment Balls, Bags, Partitions, and Permutations Thanks, shouldn't k start from 1. Mar 22 accepted Balls, Bags, Partitions, and Permutations Mar 21 asked Balls, Bags, Partitions, and Permutations Mar 13 comment Probability of having exactly 1 pair from drawing 5 cards please note that the question states "pair means same color or same type". Are you not counting for 2 pairs also then( 1 pair of same type and 1 pair of same color - as per pigeon hole principle - we have only 4 colors and selecting 5 balls )? Mar 13 answered Probability of having exactly 1 pair from drawing 5 cards Mar 10 comment Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) perfect. Thanks a lot. Regarding the solution proposed in the question, i was thinking like Gerry at that time( but, now i checked the question once again and you're right ). I'm still interested in what happens in that case. I'll read about Bell numbers and see. Mar 10 awarded Scholar Mar 10 accepted Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) Mar 10 revised Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) Original Problem Statement( verbatim ) from Stanely Mar 10 comment Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) @GerryMyerson, I was thinking the same. After reading the comment by Marc i checked the question once again( in the supplement ) and found out that i was wrong( please look at the modified example in question statement ). But, anyway, we're solving another problem, then. I'll read about Bell numbers. Thanks. Mar 8 asked Counting ways to arrange envelopes by inclusion (from Stanley's Enumerative Combinatorics) Feb 28 answered Formula for $\sum _{i=1}^n (n+1-i) (n-i)$ Feb 21 answered Number of partitions of $n$ with $k$ parts equals the number of partitions of $n + \binom k {2}$