A restaurant offers 4 different choices of soup, 2 different salads, 7 different main courses, and 7 different sides. The menu allows you to order one main course; a soup, a salad, or both; and two sides.
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First you choose one of the 7 main courses. There are 7 ways to do that. Then you choose 2 of the 7 sides. There are 7*6, ways to do that. Then you choose either a soup, a salad, or both. There are 4 ways to choose 1 of the 4 soups, 2 ways to choose 1 of the 2 salads, and 4*2 ways to choose 1 of the 4 soups and 1 of the 2 salads.
So, the total number of possible orders is:
7 * 7 * 6 * (4 + 2 + 4*2)
That's equal to 4116, so there are 4116 possible different orders.
Hope that helps :)
Edit:
The first answer is incorrect. The number of ways to choose 2 of the 7 sides is 7*6, not 7², since you can't choose the same side twice. Also, the question states that you can choose either a soup or a salad or both, so you need to multiply by 4+2+4*2, not just 4*2. The 4*2 would be correct if you had to choose both a soup and a salad.
So, the total number of possible orders is:
7 * 7 * 6 * (4 + 2 + 4*2)
That's equal to 4116, so there are 4116 possible different orders.
Hope that helps :)
Edit:
The first answer is incorrect. The number of ways to choose 2 of the 7 sides is 7*6, not 7², since you can't choose the same side twice. Also, the question states that you can choose either a soup or a salad or both, so you need to multiply by 4+2+4*2, not just 4*2. The 4*2 would be correct if you had to choose both a soup and a salad.
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7* 4 * 2 * 7² = 2744 possible choices