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How many (5)-digit numbers can be formed from digits (0,1,2,3,4,5,6,7) without repetition and divisible by (4)?अंकों (0,1,2,3,4,5,6,7) से बिना पुनरावृत्ति के (5) अंकों की कितनी संख्याएँ बनेंगी जो (4) से विभाज्य हों?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (780)(780)
There are (14) valid ordered endings; endings without (0) give (5\cdot5P2) and endings with (0) give (6P3). For divisibility by (4), check the last two digits.अंतिम दो अंकों के (14) वैध क्रम हैं; जिनमें (0) नहीं है उनके लिए (5\cdot5P2) और जिनमें (0) है उनके लिए (6P3) गिनें। (4) से विभाज्यता में अंतिम दो अंक देखें।
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