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!) xx 2`

= 5!

= 120

Case II: Numbers are formed from 2, 2, 3, 3 and any one of 4 or 5

Number of such numbers = `(5!)/(2!2!) xx 2`

= 60

Required number = 120 + 60

= 180

∴ 180 distinct 5 digit numbers can be formed using the digit 3, 2, 3, 2, 4, 5.