Question 1098001
There are {{{11*10*9*8*7}}} ordered lists of {{{5}}} appetizers that can be written, but each set of {{{5}}} appetizers would be repeated in different order in {{{5*4*3*2}}} lists.
So, there are {{{11*10*9*8*7/(2*3*4*5)}}} different sets of {{{5}}} appetizers that can be selected, from the {{{11}}} appetizers available.
 
There are {{{4)}}} different sets of {{{3}}} main courses that can be selected from the {{{4}}} main courses available. (It is just a question of deciding which of the 4 main courses to exclude).
 
There are {{{9*8*7/(2*3)}}} different sets of {{{3}}} desserts that can be selected from the {{{9}}} desserts available.
 
Combining the possible choices for appetizer, main course, and dessets selections, the number of posssible banquet menus is
{{{(11*10*9*8*7/(2*3*4*5))*4*(9*8*7/(2*3))=11*7*(5*2)*(3*3)*(4*2)*4*9*8*7/(5*2*3*3*4*2)}}} .
Simplifying, you get
{{{11*7*7*cross(5*2)*cross(3*3)*cross(4*2)*4*9*8/(cross(5*2)*cross(3*3)*cross(4*2))=11*49*4*9*8=highlight(155232)}}}