Question
Download Solution PDFयदि n - 1P3 ∶ n + 1P3 = 5 ∶ 12 हो तो n क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFइस्तेमाल किया गया सूत्र:
गणना:
दिया गया है कि
n - 1P3 ∶ n + 1P3 = 5 ∶ 12
हम जानते हैं कि,
⇒
⇒
⇒
⇒ 12n2 - 60n + 72 = 5n2 + 5n
⇒ 7n2 - 65n + 72 = 0
⇒ 7n2 - 56n - 9n + 72 = 0
⇒ (n - 8)(7n - 9) = 0
⇒ n = 8
अतिरिक्त जानकारी
क्रमचयों की संख्या:
एक समय में r लिए गए n चीजों के सभी क्रमपरिवर्तनों की संख्या द्वारा दी गई है:
nPr = n!/(n - r)!
संयोजन:
विभिन्न समूहों या चयनों में से प्रत्येक, जो कई या सभी वस्तुओं को मिलाकर बना सकते हैं, समुच्चय कहलाते हैं।
संयोजनों की संख्या:
n चीजों के सभी संयोजनों की संख्या, एक समय में r ली जाती है:
nCr = n! /(r!) (n - r)!
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