how many three digit numbers can be formed under each condition?

Question

a) The leading digit can not be 0.

 

b) The leading digit can not be 0 and no repetition of digits is allowed.

 

c) The leading digit can not be 0 and the number must be a multiple of 5.

Answer 1

digits are 0,1,2,3,4,5,6,7,8,9

a)  first digit-9 choices because you can't use 0

     second digit-10 choices

     third digit-10 choices

     9*10*10=900

 

b) first digit-9 choices (no 0)

    second digit-9 choices (you used one digit and there are no repeats)

    third digit-8 choices (you used two digits and no repeats)

    9*9*8=648

 

c) first digit-9 choices (no 0)

    second digit-10 choices

    third digit-2 choices (last digit must be 0 or 5)

    9*10*2=180