"5 pairs of shoes with distinct colours are to be arranged in a row. In how many ways can they be arranged if all the left shoes are together and all the right shoes are together. Shoes of the same colour cannot be next to each other".
I separated the shoes into 2 groups left and right shoes respectively. Then, i realised you can shuffle each shoe in both groups 5! so my workings turned out to be 2! x 5! x 5! = 28800.
My problem is right now whenever a shoe from the left group is at the end and is the same colour as the first shoe from the right group. I dont know how to take care of that scenario.
Best Answer
Choose one left, one right from different pairs, and arrange them as L-R or R-L as dividers, thus $5*4*2 =40$ ways for dividers
Now just multiply by $4!4!$ for the remaining pairs to get $40*4!4!=23040$ total ways