Testwiki:Reference desk/Archives/Mathematics/2019 June 20

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June 20

Partitioning

Hello.

I'm looking for a ball-park order of magnitude for the number of ways that 70 can be expressed as the sum of 9 zero or positive integers, without the requirement that the individual values be unique (so 70 0 0 0 0 0 0 0 0 and 0 0 0 0 0 0 0 0 70 are both fine and count as two distinct solutions)

Thank you — Preceding unsigned comment added by 2A01:E34:EF5E:4640:91AD:2245:5820:B826 (talk) 15:38, 20 June 2019 (UTC)

See Stars and bars (combinatorics). The value you're looking for then is $(\genfrac{}{}{0ex}{}{70+9-1}{9-1})=(\genfrac{}{}{0ex}{}{78}{8})=23,446,881,315.$ –Deacon Vorbis (carbon • videos) 16:27, 20 June 2019 (UTC)

perfect, thanks — Preceding unsigned comment added by 2A01:E34:EF5E:4640:759E:2A4E:4713:9D1B (talk) 19:59, 23 June 2019 (UTC)

Super Mario Odyssey - Scale?

What is Mario's height as is defined by his appearance in Super Mario Odyssey? SMODYScale.png --Arima (talk) 22:27, 20 June 2019 (UTC)