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  • A restaurant offers a menu with 4 appetizers, 10 main courses, and 6 desserts. In how many ways can a customer choose two appetizers, two main courses, and two desserts?<

A restaurant offers a menu with 4 appetizers, 10 main courses, and 6 desserts. In how many ways can a customer choose two appetizers, two main courses, and two desserts?

 

Option: 1

6050


Option: 2

1080


Option: 3

8096


Option: 4

4050


Answers (1)

best_answer

To calculate the number of ways a customer can choose two appetizers, two main courses, and two desserts, we need to multiply the number of options for each category.

Number of ways to choose two appetizers:

\mathrm{C(4,2)=4 ! /(2 ! \times(4-2) !)=4 ! /(2 ! \times 2 !)=(4 \times 3) /(2 \times 1)=6}

Number of ways to choose two main courses:

\mathrm{C(10,2)=10 ! /(2 ! \times(10-2) !)=10 ! /(2 ! \times 8 !)=(10 \times 9) /(2 \times 1)=45}

Number of ways to choose two desserts:

\mathrm{C(6,2)=6 ! /(2 ! \times(6-2) !)=6 ! /(2 ! \times 4 !)=(6 \times 5) /(2 \times 1)=15}

To calculate the total number of ways, we multiply these three numbers together:

\mathrm{\text { Total number of ways }=6 \times 45 \times 15=4050}

Therefore, there are 4050 ways for a customer to choose two appetizers, two main courses, and two desserts from the given menu.


 

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