Question Number 74003 by mhmd last updated on 17/Nov/19
$${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$
Commented by mr W last updated on 17/Nov/19
$${using}\:{C}_{{r}} ^{{n}} ={C}_{{n}−{r}} ^{{n}} \\ $$$${C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \\ $$$$={C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{8}} ^{\mathrm{15}} −{C}_{\mathrm{9}} ^{\mathrm{15}} \\ $$$$=\mathrm{0} \\ $$