find n if 2nC3=24 nC4 find nC2 - Maths - Permutations and Combinations

Question

find n if 2nC3=24 nC4 find nC2?

Ashwini Kumar · Accepted Answer

Dear Student,

Please find below the solution to the asked query:
2nC3=24×nC4⇒2n!3!×2n-3!=24×n!4!×n-4!⇒2n2n-12n-21×2×3=24×n×n-1n-2n-31×2×3×4⇒16×2n2n-12n-2=n×n-1n-2n-3⇒16×2n×2n-1×2n-1=n×n-1n-2n-3⇒13×22n-1=n-2n-3⇒22n-1=3n-2n-3⇒4n-2=3n2-5n+6⇒4n-2=3n2-15n+18⇒3n2-19n+20=0⇒3n2-15n-4n+20=0⇒3nn-5-4n-5=0⇒n-53n-4=0⇒n-5=0  or  3n-4=0⇒n=5, 43But n can not be fraction
∴n=5

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find n if 2nC3=24 .nC4 find nC2?