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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 one dessert?</

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 one dessert?

 

Option: 1

1620


Option: 2

2800


Option: 3

7890


Option: 4

4562


Answers (1)

best_answer

To calculate the number of ways a customer can choose two appetizers, two main courses, and one dessert, 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 one dessert: 6

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

\mathrm{\text { Total number of ways }=6 \times 45 \times 6=1620}

Therefore, there are 1620 ways for a customer to choose two appetizers, two main courses, and one dessert from the given menu

 

Posted by

Rishabh

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