5-digit lock

Transcript

5-digit lockHow many passwords is possible in a 5-digit lock? If you can’t solve a problem, try to find a simpler version of the problem that you can solve. This technique can come in handy many times. Let’s consider a 2-digit lock Our digits are 0 to 9, so total 10 digits First digit can have 10 options Let’s consider all of it If First Digit is 0 All possible passwords are 01, 02, 03, 04, 05, 06, 07, 08, 09, 00 So, 10 cases Similarly, If First Digit is 1 All possible passwords are 11, 12, 13, 14, 15, 16, 17, 18, 19, 10 So, 10 cases Similarly, for all remaining eight digits (2 to 9) Total possible cases in 2-digit lock = 10 × 10 = 100 For a 3-digit lock First digit can have 10 options Second digit can have 10 options Third digit can have 10 options Thus, Total possible cases in 3-digit lock = 10 × 10 × 10 = 1,000 We can try listing some 000, 001, 002, 003,…. …., 098, 099 100, 101, 102, 103,… …., 198, 199 … 900, 901, 902, 903,… …, 998, 999 For a 5-digit lock Total possible cases in 5-digit lock = 10 × 10 × 10 × 10 × 10 = 1,00,000