Solve the problem by applying the fundamental counting principle. an apartment complex offers apartments with four different options, designated by a through d. aequalsnumber of bedrooms (one through four) bequalsnumber of bathrooms (one through three) cequalsfloor (first through fifth) dequalsoutdoor additions (balcony or no balcony) how many apartment options are available?

We have been given that an apartment complex offers apartments with four different options, designated by a through  d.

From the given directions we have

Therefore, from the fundamental theorem of counting principle number of available apartments are

Hence, 120 apartments options are available.

y-y1=4(x-x1)

step-by-step explanation:

this is point-slope form since you only have 4 as the slope it goes in place of m

hope this : )

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for