Question

Which of the following situation is represented by below tree diagram?

• A. 3 shirt options, 6 pants options, and 12 shoe options
• B. 3 shirt options, 2 pants options, and 2 shoe options
• C. 2 shirt options, 3 pants options, and 1 shoe option
  

Answer 1

The correct option is B

3 shirt options, 2 pants options, and 2 shoe options

In the above tree diagram,
$\bullet$ Number of shirt options: $3$ (T-shirt, Polo Shirt and Sweater)
$\bullet$ Number of pant options: $2$ (Jeans and Khaki)
$\bullet$ Number of shoe options: $2$ (Sneakers and Sandals)

$\therefore$ Option (b.) is the correct one.

$\underset{–}{\text{Remarks:}}$
From the given tree diagram, we can observe that total $12$ outfits are possible if we have 3 shirt options, 2 pants options, and 2 shoe options. And, the possible outfits are
1. T-shirt+Jeans+Sneakers
2. T-shirt+Jeans+Sandals
3. T-shirt+Khakis+Sneakers
4. T-shirt+Khakis+Sandals
5. Polo Shirt+Jeans+Sneakers
6. Polo Shirt+Jeans+Sandals
7. Polo Shirt+Khakis+Sneakers
8. Polo Shirt+Khakis+Sandals
9. Sweater+Jeans+Sneakers
10. Sweater+Jeans+Sandals
11. Sweater+Khakis+Sneakers
12. Sweater+Khakis+Sandals

$\underset{–}{\text{An alternate way of finding total number of outfits}}$
By multiplying 3 shirt options, 2 pants options and 2 shoe options, we can find total outfits.
$\Rightarrow$ Total outfits = $3\times 2\times 2=12$