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Question Number 74003 by mhmd last updated on 17/Nov/19
find C_8 ^(15) +C_9 ^(15) −C_7 ^(15) −C_6 ^(15)  ?  pleas help me sir ?
$${find}\:{C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \:? \\ $$$${pleas}\:{help}\:{me}\:{sir}\:? \\ $$
Commented by mr W last updated on 17/Nov/19
using C_r ^n =C_(n−r) ^n   C_8 ^(15) +C_9 ^(15) −C_7 ^(15) −C_6 ^(15)   =C_8 ^(15) +C_9 ^(15) −C_8 ^(15) −C_9 ^(15)   =0
$${using}\:{C}_{{r}} ^{{n}} ={C}_{{n}−{r}} ^{{n}} \\ $$$${C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{7}} ^{\mathrm{15}} −{C}_{\mathrm{6}} ^{\mathrm{15}} \\ $$$$={C}_{\mathrm{8}} ^{\mathrm{15}} +{C}_{\mathrm{9}} ^{\mathrm{15}} −{C}_{\mathrm{8}} ^{\mathrm{15}} −{C}_{\mathrm{9}} ^{\mathrm{15}} \\ $$$$=\mathrm{0} \\ $$

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