Question

Establish the number of ways in which 7 different books can be placed on a bookshelf if 2 particular books must occupy the end positions and 3 of the remaining books are not to be placed together.

Answer 1

5! - 3! x 3!

Answer 2

5!-3! x 3! =84 and that is not the answer.

Answer 3

multiply it by 2

Answer 4

as you can permute the ennds in 2! ways

Answer 5

Can you draw it, or explain your steps?

Answer 6

(5! - 3! x 3!) x 2!

Answer 7

im thinking its more like 2*3*2*2*1*1*1
reasoning
the first slot can only be filled with 2 books
the 2nd slot can only be filled with 3 books
cause out of 5 books the 3 books must occupy the 1st, 3rd and5th slots
3rd can only be filled with remaining 2 books,
4 is filled with remaining 2 books from the 3
and last remaining books fill the last 3 spots

Answer 8

you fixed the ends with 2 books

Answer 9

remaining 5 books u can permute in 5! ways

Answer 10

yep.

Answer 11

but out of these 5! ways, there will be few arrangements, where the 3 books are together which u dont want

Answer 12

these form 3! x 3! ways

Answer 13

just subtract these from 5! to get the arrangements without these 3 books together

Answer 14

how do you know/where do you get 3 books are together is 3! x 3! ways?

Answer 15

good q

Answer 16

5 books

Answer 17

you can arrange them such that 3 books are always together in 3! x 3! ways

Answer 18

how ?

thats ur q, correct ?

Answer 19

yes.

Answer 20

say those are the 3 books u want always together