Question
Download Solution PDFयदि C(3n, 2n) = C(3n, 2n - 7) है, तो C(n, n - 5) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
संचय
\(\displaystyle ^n C_r=\frac{n !}{r ! (n-r) !}\),
जहां,
nCr = संचयों की संख्या
n = समुच्चय में वस्तुओं की कुल संख्या
nCx = nCy ⇒ x = y या x + y = n
गणना:
दिया है:
C(3n, 2n) = C(3n, 2n - 7)
⇒ 3nC2n = 3nC2n-7
⇒ 2n + 2n - 7 = 3n
⇒ 4n - 3n = 7
⇒ n = 7
C(n, n - 5) का मान = nCn-5 = 7C7-5 = 7C2
7C2 = \(\displaystyle \frac{7!}{2!\times5!}\) = 21
C(n, n - 5) का मान = 21
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