Question Number 42224 by 33 last updated on 20/Aug/18
$${a}\:+\:{b}\:+\:{c}\:=\:\mathrm{180}\: \\ $$$${a},{b},{c}\:\in\:\mathbb{N} \\ $$$${number}\:{of}\:{triplets}\:{possible} \\ $$$$\left({a},{b},{c}\right)\:{for}\:{the}\:{above} \\ $$$${equation}\:{are}\:? \\ $$$$\left(\:{the}\:{order}\:{of}\:{a},{b},{c}\:\:{doesn}'{t}\right. \\ $$$$\left.{matter}\right) \\ $$
Commented by rahul 19 last updated on 20/Aug/18
$$\mathrm{15},\mathrm{931}\:\:\:\:=\:\:\:\left(\mathrm{179}_{\mathrm{C}_{\mathrm{2}} } \right)\:\:\:\:\:? \\ $$
Commented by 33 last updated on 20/Aug/18
$${answer}\:{is}\:{not}\:{known}. \\ $$$${please} \\ $$$${can}\:{you}\:{show}\:{the}\:{working}. \\ $$
Commented by rahul 19 last updated on 20/Aug/18
$$\mathrm{There}\:\mathrm{is}\:\mathrm{a}\:\mathrm{direct}\:\mathrm{formula}\:\mathrm{for}\:+\mathrm{ve} \\ $$$$\mathrm{integers}\::\:\mathrm{n}−\mathrm{1}_{\mathrm{C}_{\mathrm{r}−\mathrm{1}} } \\ $$$$\mathrm{For}\:\mathrm{non}.\:\mathrm{negative}\:\mathrm{integers}\::\:\mathrm{n}+\mathrm{r}−\mathrm{1}_{\mathrm{C}_{\mathrm{r}−\mathrm{1}} } \\ $$$$\mathrm{They}\:\mathrm{come}\:\mathrm{from}\:\mathrm{multinomeal}\:\mathrm{theorem}. \\ $$$$\mathrm{So}\:\mathrm{in}\:\mathrm{this}\:\mathrm{case}\:\mathrm{179}−\mathrm{1}_{\mathrm{C}_{\mathrm{3}−\mathrm{1}} } . \\ $$
Commented by 33 last updated on 20/Aug/18
$${in}\:{case}\:{we}\:{dont}\:{know}\:{the} \\ $$$${formula}? \\ $$
Commented by Tinkutara last updated on 20/Aug/18
See Q. 22040