Halloween Counting

How many ways are there to arrange the letters in the word "HALLOWEEN"?

• $9!$
  

• $\frac{9!}{2!}$

• $\frac{9!}{4!}$

• $\frac{9!}{2!2!}$

There are 10 students in our class dressed in their Halloween costumes. How many ways are there to award 1st, 2nd, and 3rd prize for costumes, if Sophia is one of the winners?

Ryan went trick-or-treating and came back with 30 different chocolate bars and 20 different sour candies. He wants to give 5 of each to Jason. How many different combinations of 5 chocolate bars and 5 sour candies can he give him?

Zameer's stash of candy includes 3 identical Twixes, 4 identical KitKats, and 2 identical boxes of Nerds. In how many different orders can he eat those 9 treats?

There are 6 scary homework problems to review. In a class of 13, with no one presenting more than once, how many different sets of homework presenters can we have (order matters)? 

The class is divided into two groups - the students who like chocolate, and the students who don't. How many distinct ways are there to divide the class into the two groups, if there are 13 students?

• 14

Which of these is your favorite Halloween candy?

• Lollipop or other hard candy

• M & M's or Skittles

• Sour Patch Kids or other gummies

• Snickers/Twix/KitKat or other chocolate bar

• Other