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CAT 2025 Slot 1 QA Question 8

Multiple choice (+3 / −1) · Modern Math · Permutation & Combination · Try it, then check the answer and solution below.

CAT 2025 Slot 1QAModern Math • Permutation & CombinationModerate
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is
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Answer and solution

Answer: A) 880

📌 Core Concept
The problem involves calculating the total number of ways to order a sandwich with multiple independent choices. We use the Multiplication Principle of counting, which states that if there are nn ways to do something and mm ways to do another thing independently, then there are n×mn \times m ways to do both.
🔢 Step-by-Step Solution
1
Types of Sandwiches: There are 5 types of sandwiches.
Options=5\text{Options} = 5
2
Bread Options: For each sandwich, there are 4 types of bread.
Options=4\text{Options} = 4
3
Size Options: For each sandwich, there are 2 size options (small or large).
Options=2\text{Options} = 2
4
Sauce Options: A customer can choose 0, 1, or 2 sauces from 6 available.
0 sauces: (60)=1\binom{6}{0} = 1 way
1 sauce: (61)=6\binom{6}{1} = 6 ways
2 sauces: (62)=6×52×1=15\binom{6}{2} = \frac{6 \times 5}{2 \times 1} = 15 ways
Total Sauce Options=1+6+15=22\text{Total Sauce Options} = 1 + 6 + 15 = 22
5
Total Combinations: Multiply the number of options for each independent choice.
Total Ways=(Types×Breads×Sizes)×Sauces=(5×4×2)×22=40×22=880\text{Total Ways} = (\text{Types} \times \text{Breads} \times \text{Sizes}) \times \text{Sauces} = (5 \times 4 \times 2) \times 22 = 40 \times 22 = 880
⚡ 30-Second Shortcut
Calculate the base combinations: 5×4×2=405 \times 4 \times 2 = 40.
Calculate sauce combinations: 1+6+15=221 + 6 + 15 = 22.
Multiply base and sauce options: 40×22=88040 \times 22 = 880.
🎯 Final Answer
Correct Answer: Option A

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