CAT 2025 Slot 1 · Quant · Question 2
CAT 2025 Slot 1 previous year question on Permutation and Combination, with the answer and a step-by-step solution.
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
- A880
- B600
- C800
- D840
Pick an option, then check.
Answer & solution
Answer: Option A
The order is built from two independent decisions, so multiply the counts.
The sandwich itself: 5 types \times 4 breads \times 2 sizes =40 ways.
The sauces: up to 2 from 6, so none, one, or two: {{}_{}^{6}{C}}_{0}+{{}_{}^{6}{C}}_{1}+{{}_{}^{6}{C}}_{2} =1+6+15=22 ways.
Total =40\times 22=880.
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