In how many ways can 5 different novels, 4 different mathematics books, and 1 biology book be arranged on a bookshelf if

Question Continuation:

if   (a) the books can be arranged in any order?  

(b) the mathematics books must be together and the novels must be together?

(a) 3628800  ways

(b) 17280 ways

Step-by-step explanation:

Given

Solving (a): In any order

This implies that there is no restriction and the novels, mathematics and biology book are just seen as books.

Total number of books is:

The number of arrangement is:

(b):

If the mathematics books are together, there are 4! different  arrangements

If the novels are together, there are 5! different arrangements

Now, there are 3 bundles.

This can be arranged in 3! ways.

Total number of arrangement is:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

if you're trying to figure out how much each ounce cost it would be 0.20

cents each ounce