A catering service offers 8 appetizers, 9 main courses, and 11 desserts. A customer is to select 4 appetizers, 7 main courses, and 10 desserts for a banquet. In how many ways can this be done?

The order doesn't matter.

$k$ objects can be chosen out of $n$ objects, when the order doesn't matter, in $C(n,k)=\dfrac{n!}{k!(n-k)!}$ ways.

$C(8,4)\cdot C(9,7)\cdot C(11,10)=\dfrac{8!}{4!4!}\cdot\dfrac{9!}{7!2!}\cdot \dfrac{11!}{10!}=\dfrac{5\cdot6\cdot7\cdot8}{2\cdot3\cdot4}\cdot\dfrac{8\cdot9}{2}\cdot11=\\=27,720$

There are 27,700 ways.

Rate answer

Wrong answer?

If your question is not fully disclosed, then try using the search on the site and find other answers on the subject Mathematics.

Find another answers

Recent questions

Mathematics, published 11.05.2023

The cost 3 kg of apples and 2 kg of orange is $3. Consider x and y as the cost per kgI oranges, respectively and draw the graph

Mathematics, published 19.03.2023

The steps Quentin took to evaluate the expression 3m-3: 3 when m=8 are shown below. 3m-3 = 3 when m = 8 3 x 8 = 24 24 – 3 = 21 21 : 3 = 7 What should Quentin have done differently in order to...

Mathematics, published 05.05.2023

If someone could answer this and give me a detailed explanation with examples about the SSS, SAS, ASA, and AAS, theorems I'd be forever grateful. I just cant seem to get the hang of it and I have...

Mathematics, published 23.03.2023

Use the equation to identify the center and radius of the circle (X+3)^2+(y-7^2=11

Mathematics, published 27.05.2023

Please help asap!!!!!!