Hi,

I can't seem to figure this one out. How many ways can the work "THINK" be arranged so that the "T" and the "H" are separated by at least one letter?

I'm trying 5x3x3x2= 90 ways but that isn't working. I think I need to use the rule of sum but I'm not quite sure how. The answer is suppose to be 72. How?

Thanks!

P.S. I have another question I'm unable to do: A locksmith has ten types of blanks for keys. Each blank has five different cutting positions and three different at each position, except for the first position, which only has two depths. How many different keys are possible with these blanks?

I'm tried 10x5x3= 150-2 = 148 but that answer is actually 1620. How is this?

Can someone please explain to me how to complete both of these questions?