help with algebra: 4 letters, without replacement, from 17 distinct letters

Question

How many ways are there of choosing
4 letters, without replacement, from 17
distinct letters,
if the order of the choices is relevant?
if the order of the choices is not relevant

Answer 1

A) If there are 17 letters, then there are 17 options for the first letter. After you've taken out that letter, there are only 16 options remaining. Each time you take away a letter, there is one fewer letter remaining in the bag. So, there are 17x16x15x14 options if the order of the choices is not relevant.

 

B) After having selected 4 letters, there are 4 choices for the first position, 3 choices for the second position, and so on following the same pattern as above. So, again, we multiply those 4 choices together. If you multiply your answer from section A) with the product you just got here, that will give you the total number of  combinations if the order is relevant because we have to account for each combination of 4 letters in A) being put into each individual slot in the order.

 

I hope that helps.