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29 Sep 2025, 09:25
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From the menu above, a restaurant offers customers two choices of appetizer and one choice each of entrée and dessert. If the appetizers must be different from each other, how many different meal combinations are available to customers?
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GMAT-Club-Forum-pyu7nmji.jpeg [ 45.1 KiB | Viewed 81 times ]
01 Oct 2025, 09:13
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Official Explanation
Find the number of choices for appetizers with the “choose” function, written as and defined for positive integers by the formula
Recall that n! means the product of all positive integers from 1 through n, inclusive. From six appetizers, we choose two, so there are 6C2 combinations, which equals
after canceling duplicate numbers in the numerator and denominator. You can also compute this by “brute force.” Label the appetizers A, B, C, D, E, and F, and then list all combinations of two appetizers as follows: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF. There are 5 + 4 + 3 + 2 + 1 = 15 combinations in all. Multiply the number of choices for appetizer by the four choices for entrée and the five choices for dessert to obtain 15 × 4 × 5 = 300 total menu combinations.
Answer: 300
GMAT-Club-Forum-9iw8dncy.png [ 32.66 KiB | Viewed 50 times ]
GMAT-Club-Forum-4gk0g4gr.png [ 6.06 KiB | Viewed 50 times ]
Find the number of choices for appetizers with the “choose” function, written as and defined for positive integers by the formula
Recall that n! means the product of all positive integers from 1 through n, inclusive. From six appetizers, we choose two, so there are 6C2 combinations, which equals
after canceling duplicate numbers in the numerator and denominator. You can also compute this by “brute force.” Label the appetizers A, B, C, D, E, and F, and then list all combinations of two appetizers as follows: AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF. There are 5 + 4 + 3 + 2 + 1 = 15 combinations in all. Multiply the number of choices for appetizer by the four choices for entrée and the five choices for dessert to obtain 15 × 4 × 5 = 300 total menu combinations.
Answer: 300
Attachment:
GMAT-Club-Forum-9iw8dncy.png [ 32.66 KiB | Viewed 50 times ]
Attachment:
GMAT-Club-Forum-4gk0g4gr.png [ 6.06 KiB | Viewed 50 times ]
