Question Number 206511 by naka3546 last updated on 17/Apr/24
Commented by mr W last updated on 17/Apr/24
$${i}\:{got}\:\mathrm{17178}. \\ $$
Commented by A5T last updated on 17/Apr/24
$$\:^{\mathrm{18}} {C}_{\mathrm{6}} −^{\mathrm{12}} {C}_{\mathrm{6}} −^{\mathrm{11}} {C}_{\mathrm{6}} +\left(^{\mathrm{5}} {C}_{\mathrm{6}} =\mathrm{0}\right)=\mathrm{17178} \\ $$
Commented by A5T last updated on 17/Apr/24
$${To}\:{choose}\:{n}\:{students}\:{generally}: \\ $$$${C}_{{n}} −^{\mathrm{12}} {C}_{{n}} −^{\mathrm{11}} {C}_{{n}} +^{\mathrm{5}} {C}_{{n}} \:\left(^{{x}} {C}_{{y}} =\mathrm{0}\:{when}\:{y}>{x}\right) \\ $$
Answered by mr W last updated on 17/Apr/24
Commented by mr W last updated on 17/Apr/24
$${using}\:{generating}\:{functions}\:... \\ $$$${to}\:{select}\:\mathrm{6}\:{students}:\:\mathrm{17178}\:{ways} \\ $$$${to}\:{select}\:\mathrm{10}\:{students}:\:\mathrm{43681}\:{ways} \\ $$$${to}\:{select}\:\mathrm{4}\:{students}:\:\mathrm{2240}\:{ways} \\ $$$$...... \\ $$