While massaging the question into some form that can be answered,
I'm assuming:
-- exactly 4 of the 10 books are math books
-- the other 6 are not math books
-- you're asking how many different ways all 10 can be arranged
on the shelf while keeping the math books all together.
If that's your question, then the answer is as follows. If that's not your question,
then the following is the answer to my question but it won't help you at all :
The 10 books are really only 7 units to be arranged ... 6 random books, and
one unit comprised of math books that might as well be glued together because
they can't separated. So the shelf arrangement involves lining up 7 things.
The first can be any one of the seven. For each of those . . .
The second one can be any one of the remaining six. For each of those . . .
The third can be any one of the remaining five. For each of those . . .
.
.
etc.
Total number of possible arrangements is (7 x 6 x 5 x 4 x 3 x 2) = 5,040 ways.
it depends on the shelf of course
Using the binomial coefficient and the 'choose' function, 10 books can be arranged 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800 different ways.
If the books have to be the correct way up and spine outwards: 7! ways =7x6x5x4x3x2x1 =5040 ways. If the books can be any way in (upside down, spine inward, etc.): (7!x4^7) ways =7x4x6x4x5x4x4x4x3x4x2x4x1x4 =82,575,360 ways
In how many distinct ways can the letters of the word MEDDLES be arranged?
Five people are to be arranged in a row to have their picture taken. In how many ways can this be done?
81
The answer depends on how many books on each subject there are.
7654321 = 7! = 5,040
it depends on the shelf of course
There are 2*5! = 240 ways.
It is a book, or set of books, giving information on many subjects or on many aspects of one subject, arranged alphabetically
The number of ways that 15 books can be arranged on a shelf is the same as the number of permutations of 15 things taken 15 at a time. This is 15 factorial, or 15!, and is 1,307,674,368,000.
9 x 8 x 7 x 6 x 5
120. You do 5*4*3*2*1=120. you multiply the number that you are given for example how many times can books 3 be arranged on a shelf you multiply 3*2*1=6 that is your answer
The number of permutations of five things taken five at a time is five factorial, or 120.
Using the binomial coefficient and the 'choose' function, 10 books can be arranged 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800 different ways.
how many ways can 8 letters be arranged