Problem Solving

In society A, it's only acceptable to name one's children one of 10 acceptable names, either for the child's first name or for the child's middle name, though some children are not given any middle name, and it's not considered acceptable to give the child the same first and middle name. When a new child is born in society A, how many possible names can the parents consider for their child?

A-110
B-100

if only first name - 10
If both first name and middle name - 10*9 (=90)
total 100
IMO B

cans wrote:if only first name - 10
If both first name and middle name - 10*9 (=90)
total 100
IMO B

I will also go with 100 with the same reasoning.

I too will go with B.

The only reason why I am writing this post is in case you were interested in an alternative solution.

___ ___ . These are the two blanks for the first and the middle name. First blank can be filled in 10 ways. Second blank can be filled in 10+1-1=10 ways. +1 as the middle name can be filled by "0 ways"(as the middle name can be left empty) while -1 indicates the name which has already been used to fill the First blank and we cant use the same name again.

Therefore, 10 * 10 = 100.