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If (f:A\to B), (A={1,2,3}), and (B={4,5,6,7}), how many one-one functions are there?यदि (f:A\to B), (A={1,2,3}), (B={4,5,6,7}), तो एकैकी फलनों की संख्या कितनी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (24)(24)
Step 1: The first element has (4) choices, the second has (3), and the third has (2). Step 2: Total one-one functions are (4\cdot3\cdot2=24). Step 3: For one-one functions, choose images without repetition.चरण 1: पहले अवयव के लिए (4) चुनाव, दूसरे के लिए (3), तीसरे के लिए (2) चुनाव हैं। चरण 2: कुल एकैकी फलन (4\cdot3\cdot2=24) होंगे। चरण 3: एकैकी फलनों में बिना दोहराव के चुनाव करें।
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