Question

How many distinct 5 digit numbers can be formed using the digits 3, 2, 3, 2, 4, 5

Answer 1

5 digit numbers are to be formed from 2, 3, 2, 3, 4, 5.

Case I: Numbers formed from 2, 2, 3, 4, 5 OR 2, 3, 3, 4, 5
Number of such numbers = `(5!)/(2!)xx2` = 5! = 120
Case II: Numbers formed from 2, 2, 3, 3 and any one of 4 or 5
Number of such numbers = `(5!)/(2!2!)xx2` = 60
Required number = 120 + 60 = 180
∴ 180 distinct 5 digit numbers can be formed using the digit 3, 2, 3, 2, 4, 5.