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If (A={1,2,3,4,5}), how many reflexive relations have exactly (9) ordered pairs?यदि (A={1,2,3,4,5}) है, तो ठीक (9) युग्मों वाले प्रतिवर्ती संबंधों की संख्या क्या होगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{20}{4})(\binom{20}{4})
Step 1: For five elements, (5) diagonal pairs are compulsory. Step 2: A relation with (9) pairs needs (9-5=4) additional non-diagonal pairs. Step 3: There are (25-5=20) non-diagonal pairs, so the answer is (\binom{20}{4}).चरण 1: पांच तत्वों के लिए (5) विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (9) युग्म चाहिए, इसलिए (9-5=4) अविकर्ण युग्म चुनने होंगे। चरण 3: अविकर्ण युग्म (25-5=20) हैं, अतः उत्तर (\binom{20}{4}) है।
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