Somebody can explain me this?:

Question

1- How many arrangements are possible using all of the letters in WHISTLER?

2-How many arrangements of the letters in WHISTLER end with a W?

Answer 1

Mercifully all the letters are distinct. There are 8 spaces that you have to fill with letters (one letter per space). There are 8 possible choices of letter to place in the first space. For each of those 8 choices, there are 7 remaining choices of letter (since you just used 1 of the original 8 letters) to place in the second space. For each of the preceding two choices, there are 6 remaining choices of letter (since you've used 2 already filling the first and second spaces) to place in the third space. Then there are 5 remaining choices of letter for the fourth space, etc. So the number of possible choices is 8*7*6*5*4*3*2*1 = 8!. In the second part, the first choice was made for you. So its the same question except with a 7 letter word rather than an 8 letter word.