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visits member for 1 year, 6 months
seen Aug 16 at 13:49

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 $n + \binom k {2}$