in how many different ways can 4 boys and 3 girls be arranged in a row such that all boys stand together and all girls stand together
There are 4! = 24 ways for the boys to stand together.
There are 3! = 6 ways for the girls t stand together.
Combining these, we get 24 x 6 = 144 ways.
However, all the boys could be on the left and all the girls on the right, or all the boys on the right and all the girls on the left, so we have a total of 2 x 144 = 288 ways.