[tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex] is the formula that calculates the total number of ways that r objects can be selected out of n.
where r!=1*2*3*...*(r-1)*r
for example
[tex]C(8, 5)= \frac{8!}{5!3!}= \frac{8*7*6*5!}{5!*3!}= \frac{8*7*6}{3*2*1}=8*7=56 [/tex] is the total number of ways we can pick 5 objects out of 8.
similarly
[tex]C(11, 9)= \frac{11!}{9!2!}= \frac{11*10*9!}{9!*2}= \frac{11*10}{2}=55 [/tex]
[tex]C(4, 2)= \frac{4!}{2!2!}= \frac{4*3*2*1}{2*2}=6 [/tex]
This means that there are 56 ways of picking the appetizers, 55 ways of picking the main courses and 6 ways of picking the desserts.
Since any of the selections of the different meals, can be combined with any selections of the other 2 meals, there are :
56*55*2=6160 ways, of selecting the 3 types of meals.
Answer: 6160
