1. an elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line. how many different ways can they sit if the elf and the dwarf insist on sitting next to each other?

a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways

2. how many ways can you order a hamburger of you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?

a. 10
b. 32
c. 64
d. 5

1. An elf, a dwarf, a hobbit, a wizard, and a man are sitting in a line. How many different ways can they sit if the elf and the dwarf insist on sitting next to each other?

a. 6 ways
b. 48 ways
c. 36 ways
d. 12 ways
e. 24 ways

elf, dwarf, hobbit, wizar, man = 5 characters

Treat first elf and dwarf as one unique character, due to they will sit next to each other.

So, calculate the number of different ways 4 can sit, i.e permutations of 4 = 4! = 4*3*2*1 = 24 ways.

Given thath elf and dwarf can exchage their position between them, the above quantity has to be multiplied by 2:

24 * 2 = 48.

option b) 48 ways

2. How many ways can you order a hamburger if you can order it with or without cheese, lettuce, tomatoes, pickles, or onions?

a. 10
b. 32
c. 64
d. 5

with or without cheese => 2 options
with or without lettuce => 2 options
                        tomatoes => 2 options
                        pickles => 2 options
                        onions  => 2 options

=> 2*2*2*2*2 = 32 ways.

option b) 32