Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 11 (Method 1) How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed? Number between 100 and 1000 will be 3 digit number 3 digit number will be formed from the digits 0, 1, 2, 3, 4, 5 But, these include numbers starting with ‘0’ like 051, 012, …etc which are actually 2 digit numbers Required numbers = Total 3 digit numbers – 3 digit number which have 0 in the beginning Total 3 digit numbers Total digits in 0, 1, 2, 3, 4, 5 = 6 n = 6 Here, we have to form 3-digit number, So, r = 3 Total number of 3 digits number = nPr = 6P3 = 6!/(6 − 3)! = 6!/3! = (6 × 5 × 4 × 3!)/3! = 6 × 5 × 4 = 120 Finding numbers that start with 0 Hence number of digit left (exclude 0 from 0, 1, 2, 3, 4, 5) = 5 So n = 5 Number of digit required = 2 r = 2 Total numbers of 3 digit number starting with ‘0’ = nPr = 5P2 = 5!/(5 − 2)! = 5!/3! = (5 × 4 × 3!)/3! = 5 × 4 = 20 Hence The required number is = Total 3 digit numbers – 3 digit number which have 0 in the beginning = 120 – 20 = 100 Example 11 (Method 2) How many numbers lying between 100 and 1000 can be formed with the digits 0, 1, 2, 3, 4, 5, if the repetition of the digits is not allowed? Number between 100 and 1000 will be 3 digit number Let the 3 digit number be If 0 is in hundred’s place, the number will be like 023, 056,etc which is a two-digit number. So, 0 is not possible in hundreds place. Number of 3 digit numbers = 5 × 5 × 4 = 100

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.