Question 1062838: Suppose there are eight different books on algebra, four different books on discrete mathematics, and five different books on history.
1-In how many ways can these books be arranged on a shelf if neither algebra books nor discrete mathematic books stay together?
2-In how many ways can these books be arranged on a shelf if only algebra books and discrete mathematics books stay together?
for first one i reached the answer
p(9,8)*p(8,4)*5!
but i don't know if it is correct
for second one i don't even know where i should start to solve it
Answer by sky1983(10)   (Show Source):
You can put this solution on YOUR website! 2. so algebra books stays together, and discrete mathematics stays together... so we consider the algebra books as one book only and the discrete mathematics books as one book only.. we add that to five history books. we have now 7 books. And we we can arrange the 7 books in 7! ways..
since the algebra books are group together, we can arrange them in 8! ways
since the discrete mathematics books are group together, we can arrange them in 4! ways
total number of ways = 7!8!4!
1. compute for the number of ways the algebra books are together and discrete mathematics are together, then subtract it from the number of ways the 17 books are arranged
total number of ways = 17! - 7!8!4!
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