Question
Download Solution PDFIf C(3n, 2n) = C(3n, 2n - 7), then what is the value of C(n, n - 5)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Combination
where,
nCr = number of combinations
n = total number of objects in the set
nCx = nCy ⇒ x = y or x + y = n
Calculation:
Given:
C(3n, 2n) = C(3n, 2n - 7)
⇒ 3nC2n = 3nC2n-7
⇒ 2n + 2n - 7 = 3n
⇒ 4n - 3n = 7
⇒ n = 7
The value of C(n, n - 5) = nCn-5 = 7C7-5 = 7C2
7C2 =
The value of C(n, n - 5) = 21
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