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In how many ways can a reflexive relation with exactly (5) ordered pairs be formed on (A={1,2,3})?समुच्चय (A={1,2,3}) पर ठीक (5) युग्मों वाला प्रतिवर्ती संबंध कितने तरीकों से बनाया जा सकता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{6}{2})(\binom{6}{2})
Step 1: The (3) diagonal pairs are compulsory. Step 2: To have (5) total pairs, choose (2) additional pairs. Step 3: There are (6) non-diagonal pairs, so the number of ways is (\binom{6}{2}).चरण 1: तीन विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (5) युग्म चाहिए, इसलिए (2) अतिरिक्त युग्म चाहिए। चरण 3: अविकर्ण युग्म (9-3=6) हैं, इसलिए (\binom{6}{2}) तरीके होंगे।
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