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 May11 comment Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ Oh! Thank you so much. You have helped me to a very great extent and I thank you for that! May11 accepted Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ May11 comment Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ First of all, many many gratitudes! I'm pretty bad in this, but there is only one thing I didn't understand. Why indeed the solutions that violates three constraints has been counted once in $35\choose 5$, 3 times in $6$ $25\choose 5$ and 3 times in $6\choose 2$ $15\choose 5$? The rest I understood, and it makes lots of sense. Thanks again!!! May11 comment Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ Yes, my mistake. I understand now why there can be two and even three violations on that constraint, but how does that reflect on the number of numbers? Thanks and sorry to bother you so much. May11 comment Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ Hi, thank you for the insight. I didn't think of the upper boundry! Now, as for you corrections. Would $n_1={20\choose 5}$? Also, I didn't understand your last paragraph. How can two of the upper bound constraints be violated at once? Or in short, I didn't understand the last paragraph idea :/ May11 asked Counting the numbers between $1$ and $1,000,000$ whose digits sum to $30$ May11 accepted How many numbers between 1 and 10,000,000 don't have the sequence 12? Inclusion-exclusion problem May11 comment How many numbers between 1 and 10,000,000 don't have the sequence 12? Inclusion-exclusion problem Regarding the number of different numbers that include 12. May11 comment How many numbers between 1 and 10,000,000 don't have the sequence 12? Inclusion-exclusion problem I see. Thank you! Very nice solution. May11 comment How many numbers between 1 and 10,000,000 don't have the sequence 12? Inclusion-exclusion problem Yes I see now. Thank you! May11 asked How many numbers between 1 and 10,000,000 don't have the sequence 12? Inclusion-exclusion problem Apr20 comment Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$ I see. Thank you for your constant help! Apr20 accepted Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$ Apr20 asked Let $(a,b)$ and $(c,d)$ be intervals in $\Bbb R$, and find an injective and surjective function from $(a,b)$ to $(c,d)$ Apr20 comment Prove that for every $p>0$, $\lim_{n\rightarrow∞}\int_n^{n+p}{\sin x\over x} = 0$ Thanks! I see you are fond of the squeeze theorem. Apr20 accepted Prove that for every $p>0$, $\lim_{n\rightarrow∞}\int_n^{n+p}{\sin x\over x} = 0$ Apr20 asked Prove that for every $p>0$, $\lim_{n\rightarrow∞}\int_n^{n+p}{\sin x\over x} = 0$ Apr19 accepted Solving the limit of integrals $\lim\limits_{q \to 0}\int_0^1{1\over{qx^3+1}} \, \operatorname{d}\!x$ Apr19 comment Solving the limit of integrals $\lim\limits_{q \to 0}\int_0^1{1\over{qx^3+1}} \, \operatorname{d}\!x$ Sadly we didn't prove this theorom in class so I still can't use it. Thanks anyway! Apr19 comment Solving the limit of integrals $\lim\limits_{q \to 0}\int_0^1{1\over{qx^3+1}} \, \operatorname{d}\!x$ Is that 'allowed'?