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On (A={1,2,3,4}), how many reflexive relations have exactly (10) ordered pairs?समुच्चय (A={1,2,3,4}) पर ठीक (10) युग्मों वाले प्रतिवर्ती संबंधों की संख्या कितनी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{12}{6})(\binom{12}{6})
Step 1: (A\times A) has (16) pairs and (4) diagonal pairs are compulsory. Step 2: To get exactly (10) pairs, choose (6) more from the (12) non-diagonal pairs. Step 3: The count is (\binom{12}{6}).चरण 1: (A\times A) में (16) युग्म हैं और (4) विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (10) युग्म चाहिए, इसलिए बाकी (6) युग्म (12) अविकर्ण युग्मों में से चुनने होंगे। चरण 3: संख्या (\binom{12}{6}) होगी।
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