Alrite, I think you have a problem with permutations and combination. Nothing to worry about you can master them in less an hour.
Here is a fast track lesson in one post.
First things first forget about factorial and formulas for permutation and combination. Keep them aside, if you really understood the whole concept you wont be needing any formulas.
Always remember:
Simultaneous actions always MULTIPLY keyword = "and"
Actions occurring not simultaneously always ADD keyword="or"
There are 3 bowls and 5 balls. In how many ways can you put 5 balls in 3 bowls. Assume each bowl can hold only 1 ball.
You can put 5 balls in 1st bowl in 5 ways
You can put 4 balls in 2st bowl in 4 ways (since one ball has already been put in 1st bowl and now you are left with 4 balls)
Similarly, you can put 3 balls in 3rd bowl in 3 ways
Since all this has to happen simultaneously,
5*4*3 = 60 ways
Now lets look at the formula 5p3 = 60 ways.
Now switch the wordings of the question.
How many 3 digit numbers can formed using letters 1, 2, 3, 4, 5. None of the digits can be repeated.
Answer is again 60.
In GMAT the question regarding digits wont be this easy. There will be some conditions, like you saw in previous questions where divisibility and other things are taken into account. I think you are pretty good at number system so you wouldnt have any problems dealing with those.
Finally, I'll answer your question about 1*5*4*3.
We have to find numbers between 50000-60000 and we have 2,3,4,5,6,7 digits. The numbers can be repeated.
_ _ _ _ _ _
In the first blank we can only put 1 number i.e. 5 because the number formed has to be between 50000 to 60000. Therefore we can arrange this only 1 ways.
Second blank we can put any number from 2-7 since the question says the number can be repeated. Therefore we have 6 options = 6 ways.
Similarly we have 6 letters for each of the 5 blanks except for the first one.
And all this has to happen simultaneously therefore 1*6*6*6*6*6
Try to do the same problem with condition that numbers cannot be repeated.
This is the best that I can do in one post. Hope this helps you, it indeed has helped me.
