SOLUTION: I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf

Question 1207619: I have $3$ different mathematics textbooks, $2$ different psychology textbooks, and $2$ different chemistry textbooks. In how many ways can I place the $7$ textbooks on a bookshelf, in a row, if all three mathematics textbooks must be together?
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.
I have 3 different mathematics textbooks, 2 different psychology textbooks,
and 2 different chemistry textbooks. In how many ways can I place the 7 textbooks
on a bookshelf, in a row, if all three mathematics textbooks must be together?
~~~~~~~~~~~~~~~~~~~

We start the solution, considering 3 Math textbook as one object. 
We have then 5 different objects, at all, and 5! = 120 possible
permutations for them.


Then we multiply 5! by 3! = 6, the number of permutations inside the set of 3 Math textbook.


Thus we come to the 


ANSWER.  There are 5!*3! = 120*6 = 720 different arrangements of the textbooks 
         on a bookshelf under the given restriction.

Solved.

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