Problem Solving

Question 1

Of the three-digit positive integers that have no digits equal
to zero, how many have two digits that are equal to each
other and the remaining digit different from the other two?
A.24
B.36
C.72
D.144
E.216

think of this as an arrangement problem -

1. digits that can be used 1-9.
2. no. of ways in which you can pick up a digit = 9, correspondingly you can pick up second digit to be used in number formation in 9 ways. ie. total ways= 9.8
3. for each way, there can be three 3-digit numbers. (for ex. if two digits picked are 1,2 resp., possible numbers will be 122, 212, 221)
4. so total possible such numbers = 72.3=216