Question

Leela went to a small garment store with her son. She wanted to buy an outfit for him. In the garment store, she found two types of shirts: Formal and Denim. There were 3 choices for formals and 4 choices for denims. There were two types of pants: Jeans and Formal, with 2 choices for each of them. Question 18 If any shirt can be worn with any pair of pants, the number of ways Leela can select an outfit for her son are a) 20 b) 24 c) 26 d) 28

Answer 1

How many ways are there to select an outfit ?

GIVEN :-

Shirts :-

• Formal - 3
• Denim - 4
• Total - 7

Pants :-

• Jeans - 2
• Formal - 2
• Total - 4

Since, the question says any shirt can be worn with any pair of pants. Therefore, there is no need to consider shirts and pants individually on the basis of its fabric to make an outfit.

We can directly calculate by the total no. of choices we have for both shirts and pants.

So,

No. of ways to select an outfit = 7 x 4 = 28 ways.

To check it, we can list down all the possible pairs.

Let :-

F - Formal

D - Denim

J - Jeans

The first item I am taking is shirt and the second is pant.

So, the pairs are as follows :-

$F_{1}J_{1} , F_{1}J_{2} , F_{1}F_{1} , F_{1}F_{2} , \\F_{2}J_{1} , F_{2}J_{2} , F_{2}F_{1} , F_{2}F_{2} ,\\F_{3}J_{1} , F_{3}J_{2} , F_{3}F_{1} , F_{3}F_{2} , \\D_{1}J_{1} , D_{1}J_{2} , D_{1}F_{1} , D_{1}F_{2} ,\\D_{2}J_{1} , D_{2}J_{2} , D_{2}F_{1} , D_{2}F_{2} ,\\D_{3}J_{1} , D_{3}J_{2} , D_{3}F_{1} , D_{3}F_{2} ,\\D_{4}J_{1} , D_{4}J_{2} , D_{4}F_{1} , D_{4}F_{2} ,$

We can see that only these combinations are possible.

So, the answer is confirmed which is 28 ways.

Answer 2

Given :   two types of shirts: Formal and Denim. There were 3 choices for formals and 4 choices  for denims. There were two types of pants: Jeans and Formal, with 2 choices for each of them

To find : If any shirt can be worn with any pair of pants, the number of ways Leela can select an outfit for her son

20

24

26

28

Solution:

shirts:

3 choices for formals and

4 choices  for denims.

=> Total available Choices for Shirt  = 3 + 4 =  7

two types of pants:

Jeans and Formal, with 2 choices for each of them

=> Total available Choices of Pants  = 2  +  2  = 4

Leela can select an outfit for her son  in  7 * 4  = 28 Ways

Leela can select an outfit for her son in 28 ways

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