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Question Number 42224 by 33 last updated on 20/Aug/18

$$a+b+c=180$$$$a,b,c\in \mathbb{N}$$$$numberoftripletspossible$$$$(a,b,c)fortheabove$$$$equationare?$$$$(theorderofa,b,c{doesn}^{\prime }t$$$$matter)$$

Commented by rahul 19 last updated on 20/Aug/18

$$15,931=\left({179}_{{\mathrm{C}}_2}\right)?$$

Commented by 33 last updated on 20/Aug/18

$$answerisnotknown.$$$$please$$$$canyoushowtheworking.$$

Commented by rahul 19 last updated on 20/Aug/18

$$\mathrm{There}\mathrm{is}\mathrm{a}\mathrm{direct}\mathrm{formula}\mathrm{for}+\mathrm{ve}$$$$\mathrm{integers}:\mathrm{n}-1_{{\mathrm{C}}_{\mathrm{r}-1}}$$$$\mathrm{For}\mathrm{non}.\mathrm{negative}\mathrm{integers}:\mathrm{n}+\mathrm{r}-1_{{\mathrm{C}}_{\mathrm{r}-1}}$$$$\mathrm{They}\mathrm{come}\mathrm{from}\mathrm{multinomeal}\mathrm{theorem}.$$$$\mathrm{So}\mathrm{in}\mathrm{this}\mathrm{case}179-1_{{\mathrm{C}}_{3-1}}.$$

Commented by 33 last updated on 20/Aug/18

$$incasewedontknowthe$$$$formula?$$

Commented by Tinkutara last updated on 20/Aug/18

See Q. 22040

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