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If (A={1,2,3,4}), how many reflexive relations contain exactly (11) ordered pairs?यदि (A={1,2,3,4}) है, तो ऐसे प्रतिवर्ती संबंधों की संख्या कितनी है जिनमें ठीक (11) युग्म हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\binom{12}{7})(\binom{12}{7})
Step 1: Four diagonal pairs are compulsory. Step 2: To have (11) total pairs, choose (7) non-diagonal pairs. Step 3: The number of ways is (\binom{12}{7}).चरण 1: चार विकर्ण युग्म अनिवार्य हैं। चरण 2: कुल (11) युग्म चाहिए, इसलिए (7) अविकर्ण युग्म चुनने होंगे। चरण 3: (12) अविकर्ण युग्मों में से (7) चुनने के तरीके (\binom{12}{7}) हैं।
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