Mattais gets dressed in the dark one morning and chooses his clothes at random. he chooses a shirt (green, red, or yellow), a pair of pants (black or blue), and a pair of shoes (checkered or red). make a tree diagram to find the sample space.

 The tree diagram is shown in the attached figure.

Step-by-step explanation: Given in the question that Mattais gets dressed in the dark one morning and chose his clothes randomly. The shirts are green, red and yellow, pants are black and blue and shoes are checkered and red.

So, the number of ways in which the dress can be chosen

= 3 × 2 × 2

= 12.

And the combinations are

(Green shirt, black pant, checkered shoes),

(Green shirt, black pant, red shoes),

(Green shirt, blue pant, checkered shoes),

(Green shirt, blue pant, red shoes),

(Red shirt, black pant, checkered shoes),

(Red shirt, black pant, red shoes),

(Red shirt, blue pant, checkered shoes),

(Red shirt, blue pant, red shoes),

(Yellow shirt, black pant, checkered shoes),

(Yellow shirt, black pant, red shoes),

(Yellow shirt, blue pant, checkered shoes),

(Yellow shirt, blue pant, red shoes).

The tree diagram is shown in the attached figure.