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Question Number 5283 by sanusihammed last updated on 04/May/16

If 8C4 = 8Cn . find the value of n

$${If}\:\:\:\:\:\:\:\:\:\mathrm{8}{C}\mathrm{4}\:=\:\mathrm{8}{Cn}\:\:.\:\:{find}\:{the}\:{value}\:{of}\:{n} \\ $$$$ \\ $$

Commented by Rasheed Soomro last updated on 05/May/16

n=4

$${n}=\mathrm{4} \\ $$

Answered by Rasheed Soomro last updated on 05/May/16

Generally if ^n C_x =^n C_k then x=k, nāˆ’k Here k=4,n=8 x=4 , 8āˆ’4=4 x=4

$$\mathrm{Generally}\:\mathrm{if}\:\:\:^{\mathrm{n}} \mathrm{C}_{\mathrm{x}} =^{\mathrm{n}} \mathrm{C}_{\mathrm{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{then}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{k},\:\mathrm{n}āˆ’\mathrm{k} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Here}\:\mathrm{k}=\mathrm{4},\mathrm{n}=\mathrm{8} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{4}\:,\:\mathrm{8}āˆ’\mathrm{4}=\mathrm{4} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{4} \\ $$

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