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.
Answer: 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.
answer: option b) 32
