Four different mathematics books, six different physics books, and two different chemistry books are to be arranged on a shelf. How many different arrangements are possible if a) The books in each particular subject must all stand together b) Only the mathematics books must stand together

a) 207,360 ways

b)8,709,120  ways

Step-by-step explanation:

Total number of subjects= 3

Number of mathematics books = 4

Number of physics books = 6

Number of chemistry books = 2

Part a:

Number of possible arrangement s= 3! 4! 6! 2!= 6*24*720*2= 207360 ways

In this we have included 3! because the books have to be placed in such a manner that the books in each particular subject must all stand together.

Part b:

Similarly the mathematics books must stand together so they are treated as

The total number of books will be

Physics books + Chemistry books+ Mathematics books= 6+2+1(treated as single) = 9

But there are 4 different mathematics books so these can be arranged in 4 ways.

Total number of ways in which these books can be arranged = 9! 4!= 8709120  ways.

answer: $34.31

step-by-step explanation:

$11.99 x 3 = $35.97

$35.97 - 10% = $32.37

$32.37 + 6% = $34.31

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere