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Madhavi goes to a shop where she finds three
different types of bread four different type of
cheese, three diff. type of butter of five
dift. types of jam. It she can make a sond-
wich wing only one item of each cateogry.
how many dift. ways does she have to prepare
a sandwich?
الر
Answers
Topic: Combinations
Given data:
Madhavi goes to a shop where she finds
- 3 different types of bread
- 4 different types of cheese
- 3 different types of butter
- 5 different types of jam
To find:
If she can make a sandwich with only one item of each category, In how many different ways does she have to prepare a sandwich?
Solution:
Step 1: As there are three different types of bread, a single type of bread can be chosen in ³С₁ ways.
Step 2: As there are four different types of cheese, a single type of cheese can be chosen in ⁴С₁ ways.
Step 3: As there are three different types of butter, a single type of butter can be chosen in ³С₁ ways.
Step 4: As there are five different types of jam, a single type of jam can be chosen in ⁵С₁ ways.
Therefore, the total number of ways in which a sandwich can be prepared with one item of each category is = ³С₁ x ⁴С₁ x ³С₁ x ⁵С₁ ways
= 3 x 4 x 3 x 5 ways
= 180 ways
Therefore, Madhavi can prepare a sandwich in 180 different ways.
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