Question

how many positive integers less than 1000 can be written using the digits 3,4,5,6? the answer key says84?

Answer 1

integers can be one digit,two digits,three digits.
no. of digits=4 (3,4,5,6)
no. of one digits=4
no. of two digits=4*4=16 (as unit placebe filled in 4 ways and tens place can be filled in four ways.e.g.,(33,34,35,36,43,44,45,46,47,etc)
no. of three digits=4*4*4=64
333,334,335,336,343,344,345,346,353,354,355,356,etc)
total no .of integers=4+16+64=?