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Combinatorics of Sandwich Customization

CAT 2025 Slot 1 · Quantitative Ability · Easy · Permutations and Combinations

This is an easy Quantitative Ability question from the CAT 2025 Slot 1 paper. It tests Permutations and Combinations. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    840

  2. B.

    800

  3. C.

    880

  4. D.

    600

Answer

C

Explanation

Choices:

  • Sandwich types: 5
  • Bread options: 4
  • Sizes: 2 (small or large)
  • Sauces options (up to 2 out of 6): (60)+(61)+(62)=1+6+15=22\binom{6}{0} + \binom{6}{1} + \binom{6}{2} = 1 + 6 + 15 = 22. Total number of ways = 5×4×2×22=40×22=8805 \times 4 \times 2 \times 22 = 40 \times 22 = 880.

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