Question

How many numbers can be formed with the digits 0,1,3,5 by using at least one digit when repetition of digits is not allowed?

Answer 1

We can form 1 digit or 2 digits or 3 digits or 4 digits numbers by using at least one digit from the given four digits.
`:.` One digit numbers = No. formed by using 1,3 or 5 - 3
Two digit numbers `= .^(4)P_(2) - .^(3)P_(1)`
`= (lfloor4)/(lfloor2) -(lfloor3)/(lfloor2)`
`= 12 - 3 = 9`
Three digit numbers `= .^(4)P_(3) - .^(3)P_(2)`
`=(lfloor4)/(lfloor1) -(lfloor3)/(lfloor1)`
`= 24 - 6 = 18`
Four digit numbers `= .^(4)P_(4) - .^(3)P_(3)`
`= 24 - 6 = 18`
`:.` The required numbers `= 3 + 9 + 18+18 = 48`.