यदि 2 पाठ्यक्रम अनिवार्य हैं, तो एक छात्र n पाठ्यक्रमों में से (n - 2) पाठ्यक्रमों को कितने तरीकों से चुन सकता है (n > 4)?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. (n - 3) (n - 4)
  2. (n - 1) (n - 2)
  3. (n - 3) (n - 4)/2
  4. (n - 2) (n - 3)/2

Answer (Detailed Solution Below)

Option 4 : (n - 2) (n - 3)/2
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व्याख्या:

दिया गया है,

पाठ्यक्रमों की संख्या, n > 4

छात्र को n पाठ्यक्रमों में से (n - 2) पाठ्यक्रम चुनने हैं, जिसमें 2 पाठ्यक्रम अनिवार्य हैं

∴ कुल पाठ्यक्रम n - 2 हैं और (n - 2) पाठ्यक्रमों में से चुने जा सकने वाले शेष पाठ्यक्रमों की कुल संख्या (n - 4) है।

∴ आवश्यक तरीकों की संख्या (n-2) C (n-4).

\(\frac{(n-2)(n-3)}{2}\)

∴ विकल्प d सही है।

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