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

880

840

600

800

✅ Correct Option: 1

An order requires 4 independent choices:

Sandwich type: $5$ ways

Bread type: $4$ ways

Size (small or large): $2$ ways

For sauces, the customer can add 0, 1, or 2 sauces out of 6 available.

Since adding sauces is optional, all three cases need to be considered:

0 sauces: ${}^{6}C_0 = 1$

1 sauce: ${}^{6}C_1 = 6$

2 sauces: ${}^{6}C_2 = 15$

Note: Combinations are used here because the order in which sauces are chosen does not matter.

Total sauce options $= 1 + 6 + 15 = 22$ ways

Since all 4 choices are independent of each other, the total number of ways to place an order:

$= 5 \times 4 \times 2 \times 22$

$= 40 \times 22$

$= 880$

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