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If 35C n + 7 = 35C 4n - 2, then all the values of n are given by?

Correct Answer: 3, 6

Explanation:

35Cn + 7 = 35C4n - 2
We know that if nCx = nCy then, Either x = y or x + y = n
Case 1: x + y = n
⇒ n + 7 + 4n - 2 = 35
⇒ 5n + 5 = 35
⇒ 5n = 30
∴ n = 6
Case 2: x = y
⇒ n + 7 = 4n - 2
⇒ 4n - n = 2 + 7
⇒ 3n = 9
∴ n = 3


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