Question

In a restaurant there are

8 starter dishes
15 main dishes
9 dessert dishes
Jane is going to choose one of the following combinations for her meal.
a starter dish and a main dish
or a main dish and a dessert dish
or a starter dish, a main dish and a dessert dish
How many different ways are there for her to choose the meal?

Answer 1

there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.

Explanation:

First, we need to find the number of different combinations of a starter dish and a main dish. This is simply the number of combinations of 2 items from 8 starters and 15 main dishes, which can be calculated using the formula for combinations:

C(8 + 15, 2) = C(23, 2) = (23 * 22) / (2 * 1) = 276

Similarly, the number of different combinations of a main dish and a dessert dish is:

C(15 + 9, 2) = C(24, 2) = (24 * 23) / (2 * 1) = 276

Finally, the number of different combinations of a starter dish, a main dish, and a dessert dish is:

C(8 + 15 + 9, 3) = C(32, 3) = (32 * 31 * 30) / (3 * 2 * 1) = 5680

In total, there are 276 + 276 + 5680 = 6232 different ways for Jane to choose her meal.