Continuing on with the GRE practice questions I have, I'm confused about how to solve the following types of probability questions.
Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?
There are 120 ways they can sit together in a row of 5 seats because 5! = 120. I'm confused as to how you would mathematically describe a situation where Martha is sitting only in the "middle" seat.
How many 3-digit positive integers are odd and do not contain the digit 5 ?
If I am correct (probably not), there are 999–99=900 3-digit positive integers (this means there are 450 odd 3-digit positive integers, I think). Of these, 100/900 will be a 5 (i.e. 5xx), 10/100 10s will be a 5 (i.e. x5x), and 1/10 1s digits will be a 5 (i.e. xx5). At this point I'm lost in numbers and it has taken me much longer than the minute I will be given to solve it. Am I missing some sort of heuristic to solving these?
Thanks for you help.