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How many (4)-digit numbers can be formed from digits (4,5,6,7,8,9) without repetition?अंकों (4,5,6,7,8,9) से बिना पुनरावृत्ति कितनी (4)-अंकीय संख्याएँ बनेंगी?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(360\)\(360\)
Four digits must be selected and arranged from the 6 given digits. Hence, the number of such numbers is \({}^6P_4=6\times5\times4\times3=360\). The value \(720\) is \(6!\), which would apply if all 6 digits were arranged, not just 4. Exam tip: use \({}^nP_r\) when order matters and repetition is not allowed.6 दिए गए अंकों में से 4 अंकों को क्रम में चुनना है। अतः कुल संख्याएँ \({}^6P_4=6\times5\times4\times3=360\) होंगी। \(720\) तब मिलता है जब सभी 6 अंकों का क्रमचय \(6!\) लिया जाए, जो यहाँ आवश्यक नहीं है। परीक्षा टिप: बिना पुनरावृत्ति और क्रम महत्त्वपूर्ण होने पर \({}^nP_r\) का प्रयोग करें।
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