Question

i have 7 books in english, 3 in french, 5 in Czech, how many ways can they all be arranged if the books of the same language have to be together

Answer 1

within the language categories we have 7! 3! 5! arrangements, independent, so they multiply together. Then we have three languages so they can be put into 3! orders, so multiply the prior number by 3!

Answer 2

consider all the book of one language as one group...arranging them = 3!
internal arrangement = 7!.5!.3!
so total arrangements 7!5!3!3!