Question

Manen’s closet has three pairs of pants (black, white and green), two shirts (green and white) and two pairs of shoes (black and white).

• a) How many different outfits can be made?

• b)   Write down the sample space.

• c)   What is the probability that if you close your eyes and choose randomly, you would   

choose:

• (i) Pants and shoes with the same colour?

• (ii) Pants and shirts with the same colour?

• (iii) Pants, shoes and shirts with the same colour?

• (iv) Pants, shoes and shirts with the different colours?

Answer 1

a)

$$\dbinom{3}{1}\dbinom{2}{1}\dbinom{2}{1}=12$$

12 different outfits can be made.

b) The sample space is

$$S=\{B_1G_2B_3, B_1G_2W_3,B_1W_2B_3,B_1W_2W_3,$$

$$W_1G_2B_3, W_1G_2W_3,W_1W_2B_3,W_1W_2W_3,$$

$$G_1G_2B_3, G_1G_2W_3,G_1W_2B_3,G_1W_2W_3\}$$

c)

(i)

$$B_1G_2B_3,B_1W_2B_3,W_1G_2W_3,W_1W_2W_3$$

$$p=\dfrac{4}{12}=\dfrac{1}{3}$$

(ii)

$$W_1W_2B_3, W_1W_2W_3, G_1G_2B_3, G_1G_2W_3$$

$$p=\dfrac{4}{12}=\dfrac{1}{3}$$

(iii)

$$W_1W_2W_3$$

$$p=\dfrac{1}{12}$$

(iv)

$$B_1G_2W_3,W_1G_2B_3,G_1W_2B_3$$

$$p=\dfrac{3}{12}=\dfrac{1}{4}$$