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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 three appetizers, two main courses, and two desserts?  <div

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

 

Option: 1

5000


Option: 2

2700


Option: 3

6500


Option: 4

9000


Answers (1)

best_answer

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

Number of ways to choose three appetizers:

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

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 }=4 \times 45 \times 15=2700}

Therefore, there are 2700 ways for a customer to choose three appetizers, two main courses, and two desserts from the given menu.

 

Posted by

himanshu.meshram

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