If Evan takes either the package of peanuts or the banana, how many different selections of three snack items can he take?

Question

Evan has two baskets containing snacks items. The first basket contains one package each of peanuts, almonds, cashews, and pretzels. The second basket contains a banana, a mango, a peach, a pear, and a plum. Evan takes one item from the first basket and two items from the second basket for his lunch. If Evan takes either the package of peanuts or the banana, how many different selections of three snack items can he take?

A. 18

B. 22

C. 36

D. 40

Answer 1

Possible outcomes for:

(1) Choosing one from the first basket (containing 4 items) and not considering the second basket:

₄C₁ = 4!/(1!(4-1)!) = 4

(2) Choosing 2 from the second basket (containing 5 items) and not considering the first basket:

₅C₂ = 5!/(2!(5-2)!) = 10

(3) Choosing a peanut from the first basket and 2 items from the second basket:

(₃C₀)(₅C₂) = 10

(4) Choosing a banana then one more item from the second basket and 1 item from the first basket:

(₄C₁)(₄C₁) = 16

(5) Remember, there are 4 outcomes from (3) and (4) that are exactly the same:

Peanut => Banana, mango

Peanut => Banana, peach

Peanut => Banana, pear

Peanut => Banana, plum

10+16-4 = 22

I choose B.