Please help me with math problem.

Question

An opinion poll was conducted by the Morris Polling Group. Respondents were classified according to their sex (M or F), political affiliation (D, I, R), and the region of the country in which they reside (NW, W, C, S). ?

 

Use the generalized multiplication principle to determine the number of possible classifications. ?

 

Thank you for helping

Answer 1

Multiplication Principle states: If an event occurs in m ways and another event occurs independently in n ways, then the two events can occur in m × n ways

 

If you have 2 possible genders, 3 possible political, and 4 possible regions, this would be 2 x 3 x 4 = 24 possible combinations.

 

If you simplify the problem to just start with the gender x political affiliation, it is easier to see how this works.

You can have 

M D

M I

M R

(3 political options for males)

F D

F I

F R

(3 political options for females)

which is a total of 6 combinations: 2 x 3 for gender/political only

 

Going the next step to include region:

You know that there are 4 possible regions for every gender/political combination so you know that there would be 4 region options for every one of the 6 gender/political combos already identified.  4 sets of 6 = 24 total combinations.

 

Hope this helps :-)