Your math teacher is packing to vacation in a warm, sunny location and she does not want to pay the extra money for checked luggage.

Question

Your math teacher is packing to vacation in a warm, sunny location and she does not want to pay the extra money for checked luggage. She needs to pack all her clothes in one small carry-on bag. She decides to take 4 different tops (a tank top, a t-shirt, and two different coloured blouses), and 3 choices for bottoms (shorts, skirt and pants). To accessorize she packs a scart

and a sweater.

a) Draw a tree diagram to represent the number of different outfits she could make if she does

not wear the scarf and sweater at the same time.

b) Use the fundamental counting principle to determine the number of different outfits for a)

c) Determine the total number of different outfits if your math teacher also includes the option of wearing the scarf and sweater at the same time. Hint: There are two cases to consider.

Answer 1

a) let the tops be T1, T2, T3, T4, and bottoms be B1, B2, B3.

she has 2 choice for accessories, scarf and sweater. and she does not wear them at same time.

scarf

/ | | \

T1 T2 T3 T4

/|\ /|\ /|\ /|\

B1 B2 B3 B1 B2 B3 B1 B2 B3 B1 B2 B3

List down the outfits [scarf, T1, B1], [scarf, T1, B2], ... etc. do the samething for sweater

b) 4 choices for tops, 3 for bottoms, 2 for accessories

4*3*2 = 24 outfits

c) think of sweater and scarf as a single accessory

in that case it 4*3*1 = 12 outfits