3 red and 2 blue books, put on shelf with red together, how many ways can you do this?

Answer 1

It depends on whether the two blue books are exactly the same and also whether the red books are the same or not. For the sake of argument, lets say they are not. Then, say the two blue books are A and B, and the red books are X,Y,Z, then you can start to permute as follows;
XYZAB
XYZBA
XZYAB
XZYBA
YXZAB
YXZBA
YZXAB
YZXBA
ZYXAB
ZYXBA
ZXYAB
ZXYBA
Which gives a count of 12 for having the red books on the left of A and B. You will get an additional 12 for having the red books in the middle of A and B, and yet another 12 for having the red books to the right of A and B. making a total of 36.

If for example, the two blue books are the same but the red ones are not, then you can divide the number by 2 to get 18. If the three red books are the same, but the two blue ones are not, then you divide by 6 to get an answer of 6. If all red books are the samer and all blue books are the same, you divide by 12 to get an answer of 3.

Good luck withg your school work!!!

Answer 2

38

Answer 3

Three. They are
bbrrr
brrrb
rrrbb

As the red books must stay together there is no other arrangement.

Answer 4

Four