Misc 5 - How many 6-digit numbers from 0, 1, 3, 5, 7, 9 - Permutation- non repeating

  1. Chapter 7 Class 11 Permutations and Combinations
  2. Serial order wise
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Misc 5 (Method 1) How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated? A number is divisible by 10 if 0 occur at the units place We need to formed 6 digit number whose unit place is fix Now we need to fill up 5 place with the remaining digit 1, 3, 5, 7, & 9 Hence, n = Number of digits = 5 & r = Number of places to fill = 5 Number of 6 digit numbers = 5P5 = 5!/(5 − 5)! = 5!/0! = 5!/1 = 5 × 4 × 3 × 2 × 1 = 120 Misc 5 (Method 2) How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated? A number is divisible by 10 if 0 occur at the units place We need to formed 6 digit number whose unit place is fix Now we need to fill up 5 place with the remaining digit 1, 3, 5, 7, & 9 Number of 6 digit numbers = 1 × 5 × 4 × 3 × 2 × 1 = 120

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