Question

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.

Answer 1

3P3 x 4P4 x 5P5 x 6 = 103,680 since there are 6 ways of arranging subjects ?

Answer 2

why times 6

Answer 3

like why are there 6 ways of arranging them.. how did you figure that out?

Answer 4

ok, ill have a go at this one , but its been like 2years since I last really did solid study of combinatorics lol

Answer 5

lolololol

Answer 6

so it should be = 3! x 4! x 5! x 3!

Answer 7

check if thats the answer, before I try to explain it

Answer 8

right

Answer 9

I dont like doing the whole nPr notation, its lazy

Answer 10

i understand how to do it, all i dont understand is why there is a second 3 factorial added to the equation

Answer 11

you consider them as seperate groups

Answer 12

you group the subjects together

Answer 13

there are n! ways of arranging n objects in a group

Answer 14

and then there are 3! ways of arranging your groups in a line

Answer 15

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}

Answer 16

it takes a little getting used to , I wasnt quite sure about it the first I saw it either

Answer 17

my teacher sucks, so I had no clue

Answer 18

it gets even more complex if you were to say arrange them in a circular loop

Answer 19

or if you only arrange a subset of them in a circle, thats about as tricky as they come !v

Answer 20

I should have done a maths degree instead of engineering lol :|

Answer 21

haha you should have!!! you are very very good at math!