GEOMETRY, MEASUREMENT, DATA ANALYSIS Permutations, combinations, and the multiplication principle for coun

Question

catering service offers 7

 appetizers, 5

 main courses, and 6

 desserts. A customer is to select 4

 appetizers, 2

 main courses, and 2

 desserts for a banquet. In how many ways can this be done?

Answer 1

Hi James,

this is a combinations problem. why? because combination do not care about the order or the set we are making. how did I know the order does not matter?

If you are answering something like"because it doesn't matter if I get (fries and onion rings) versus (onion rings and fries) as long as they both are on the table :) then you got it right!

now the combination law goes as follows: C_rⁿ = n! / r!(n-r)!

where n is the total number of items in the category and r is the subset.

example:

for the appetizers n=7, r=4,

so applying the law of combinations for the appetizer gives:

number of ways for ordering the appetizers = 7!/ 4! (7-4)! = 7*6*5/3*2*1 = 35

now your turn, what is n and r for the main course? what are the number of ways for ordering the main course?

what is n and r for the dessert? what are the number of ways for ordering the dessert?

we apply the law for all of the three courses and multiply the the three numbers to get the answer.

now I want you to do the math and check your answer ;)

note: this question should be listed under statistics.

If you like my explanation give me a 5 star and if you get it right I give you a 5 star too :)