Dear Student, C3n = 20n!3! (n-3)!=20n!= 20×3!×(n-3)!n!=20×6×(n-3)!n×(n-1)(n-2)(n-3)! = 20×6×(n-3)!n(n-1)(n-2) =120From above equation it is clear thatn=6,6(6-1)(6-2)=6×5×4=120therefore n=6 Regards

↵Find n if ⁿC₃=20

Dear Student,

{}^{n}C_{3} = 20 \frac{n!}{3! . (n - 3)!} = 20 n! = 20 \times 3! \times (n - 3)! n! = 20 \times 6 \times (n - 3)! n \times (n - 1) (n - 2) (n - 3)! = 20 \times 6 \times (n - 3)! n (n - 1) (n - 2) = 120 F r o m a b o v e e q u a t i o n i t i s c l e a r t h a t n = 6, 6 (6 - 1) (6 - 2) = 6 \times 5 \times 4 = 120 t h e r e f o r e n = 6 . .

Regards

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↵Find n if nC3=20

↵Find n if ⁿC₃=20