Find the number of ways in which 3 different history books, 4 different English books, and 5 different Algebra books can be arranged on a shelf so that the books in a given subject are grouped together.

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Find the number of ways in which 3 different history books, 4 different English books, and 5 different Algebra books can be arranged on a shelf so that the books in a given subject are grouped together.

Mathematics
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3P3 x 4P4 x 5P5 x 6 = 103,680 since there are 6 ways of arranging subjects ?
why times 6
like why are there 6 ways of arranging them.. how did you figure that out?

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Other answers:

ok, ill have a go at this one , but its been like 2years since I last really did solid study of combinatorics lol
lolololol
so it should be = 3! x 4! x 5! x 3!
check if thats the answer, before I try to explain it
right
I dont like doing the whole nPr notation, its lazy
i understand how to do it, all i dont understand is why there is a second 3 factorial added to the equation
you consider them as seperate groups
you group the subjects together
there are n! ways of arranging n objects in a group
and then there are 3! ways of arranging your groups in a line
there are 6 ways of arranging the subjects as if you have a, b and c , you can arrange them as {a,b,c},{a,c,b},{b,a,c},{b,c,a},{c,a,b}{c,b,a}
it takes a little getting used to , I wasnt quite sure about it the first I saw it either
my teacher sucks, so I had no clue
it gets even more complex if you were to say arrange them in a circular loop
or if you only arrange a subset of them in a circle, thats about as tricky as they come !v
I should have done a maths degree instead of engineering lol :|
haha you should have!!! you are very very good at math!

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