NinetynineCAT 2025 Slot 1 QA Q2 Permutations & Probability
Question 2 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked 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
Answer: (A) 880 Permutations & Probability MCQ
Solution
- Sandwich choices: \(5 \times 4 \times 2 = 40\) (type, bread, size).
- Sauces (up to 2 of 6): \(\binom{6}{0} + \binom{6}{1} + \binom{6}{2} = 1 + 6 + 15 = 22\).
- Total orders \(= 40 \times 22 = 880\).
Shortcut. 'Up to 2' includes choosing none, so the sauce count is 22, not 21.