Those letters can be used to spell "seaport".
can this be love?
Six.
The rack is to hold your letters. It allows you to see and arrange your letters, yet does not let your opponent see your letters.
120 ways
There is no 8 letter word that can be made from the letters in "in and out". Words that can be made from those letters are:aadaidanandantataudioauditauntautodauntdindintdodondonnadonutdotdunduoIidininnintoioniotaitnationnitnonodnotnounnunnutoatonouttadtantintotoadtontunaundounionunitunto
The number of arrangements of the letters PARTY, if the first letter must be an A is the same as the number of arrangements of the letters PRTY, and that is 4 factorial, or 24.
If you have three DIFFERENT letters, you can arrange them in 3! = 1 x 2 x 3 = 6 different ways.
It is 6!/3! = 6*5*4 = 120 ways
Third (exactly 5 letters)
Consider "qu" to be a single letter and then you have 4 letters to arrange in 4 slots. For the first slot you have 4 choices, the next you have 3, and so on. So the number of ways is 4*3*2*1 = 24.
There is no 12-letter anagram of SRNUGTUAFEAR. There are many meaningless phrases such as "a gaunt surfer" and "fungus errata".
If all the letters of the word are different then the answer is 8! = 8*7*6* 5 *4*3*2*1 = 40320.