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If (A) has (5) elements, how many reflexive relations have exactly (12) ordered pairs?यदि (A) में (5) तत्व हैं, तो ऐसे प्रतिवर्ती संबंधों की संख्या कितनी है जिनमें ठीक (12) युग्म हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{20}{7})(\binom{20}{7})
Step 1: On a five-element set, (5) diagonal pairs are compulsory. Step 2: To have exactly (12) pairs, choose (7) non-diagonal pairs. Step 3: There are (25-5=20) non-diagonal pairs, so the number is (\binom{20}{7}).चरण 1: पांच तत्वों पर (5) विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (12) युग्म चाहिए, इसलिए (7) अविकर्ण युग्म चुनने होंगे। चरण 3: अविकर्ण युग्म (25-5=20) हैं, अतः संख्या (\binom{20}{7}) है।
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