If (n2–n)C2 = (n2–n)C4 = 120 then find the value of n.

1.	If (n2–n)C2 = (n2–n)C4 = 120 then find the value of n.
Answer» Given: ^(n2–n)C₂ = ^(n2–n)C₄ = 120 Need to find: Value of n ^(n2–n)C₂ =^(n2–n)C₄ = 120 We know, One of the property of combination is: If ⁿC_r = ⁿC_t, then, (i) r = t OR (ii) r + t = n Applying property (ii) we get, n² – n = 2 + 4 = 6 n² – n – 6 = 0 n² – 3n + 2n – 6 = 0 n(n – 3) + 2(n – 3) = 0 (n – 3) (n + 2) = 0 So, the value of n is either 3 or -2.

Answer»

Given: ^(n2–n)C₂ = ^(n2–n)C₄ = 120

Need to find: Value of n

^(n2–n)C₂ =^(n2–n)C₄ = 120

We know,

One of the property of combination is: If ⁿC_r = ⁿC_t, then,

(i) r = t OR

(ii) r + t = n

Applying property

(ii) we get, n² – n = 2 + 4 = 6

n² – n – 6 = 0

n² – 3n + 2n – 6 = 0

n(n – 3) + 2(n – 3) = 0

(n – 3) (n + 2) = 0

So, the value of n is either 3 or -2.

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