probability question

Question

Jon is packing for a trip. He has packed 2 pairs of pants, 4 shirts, and 2 pairs of shoes. In the space below, create a tree diagram, table, or list to show the sample space representing his outfit combinations and determine how many outfits can be made.

Answer 1

Jon could wear pants₁ or pants₂. No matter which pants he wears, he has four shirts to choose from, so the combinations look like this:

pants₁ shirt₁

pants₁ shirt₂

pants₁ shirt₃

pants₁ shirt₄

pants₂ shirt₁

pants₂ shirt₂

pants₂ shirt₃

pants₂ shirt₄

That's eight combinations. 2 pants * 4 shirts = 8 combinations.

Now, no matter which combination he chooses, he can wear one of two pairs of shoes. Now, the combinations look like this:

pants₁ shirt₁ shoes₁

pants₁ shirt₁ shoes₂

pants₁ shirt₂ shoes₁

pants₁ shirt₂ shoes₂

pants₁ shirt₃ shoes₁

pants₁ shirt₃ shoes₂

pants₁ shirt₄ shoes₁

pants₁ shirt₄ shoes₂

pants₂ shirt₁ shoes₁

pants₂ shirt₁ shoes₂

pants₂ shirt₂ shoes₁

pants₂ shirt₂ shoes₂

pants₂ shirt₃ shoes₁

pants₂ shirt₃ shoes₂

pants₂ shirt₄ shoes₁

pants₂ shirt₄ shoes₂

That's sixteen combinations. 2 pants * 4 shirts * 2 shoes = 16 combinations.

Answer 2

Pants 1 shirt 1 shoes 1

Pants 1 shirt 1 shoes 2

Pants 1 shirt 2 shoes 1

Pants 1 shirt 2 shoes 2

Pants 1 shirt 3 shoes 1

Pants 1 shirt 3 shoes 2

Pants 1 shirt 4 shoes 1

Pants 1 shirt 4 shoes 2

Pants 2 shirt 1 shoes 1

Pants 2 shirt 1 shoes 2

Pants 2 shirt 2 shoes 1

Pants 2 shirt 2 shoes 2

Pants 2 shirt 3 shoes 1

Pants 2 shirt 3 shoes 2

Pants 2 shirt 4 shoes 1

Pants 2 shirt 4 shoes 2

2*4*2 = 16 combinations