# Probability and Statistics - Permutations questionWatch

#1
A library contains 4 identical copies of book A, 2 identical copies of book B and 5 identical copies of
book C. These 11 books are arranged on a shelf in the library.

ii) Calculate the number of different arrangements if all the books A are next to each other and none
of the books B are next to each other.

The question is from CIE 9709 May-June 2017 paper 62. Any help will be appreciated.
0
1 week ago
#2
consider [AAAA] as a single object
you have to arrange [AAAA] B B C C C C C
so that B are not together

one method is
arrange [AAAA] and the 5 C's first
e.g * [AAAA] * C * C * C * C * C *
this creates 7 places (marked *) for the B's.
hence number of arrangements is found

another method is
find number of arrangements when B's are together, i.e of [AAAA] [BB] C C C C C
subtract from no restrictions on B's & A's together
Last edited by BobbJo; 1 week ago
0
#3
I have one question. I saw in the examiner report that an error is to arrange AAAA and multiply with 4! . How come AAAA doesn't have to be arranged? Is it because they are identical?
(Original post by BobbJo)
consider [AAAA] as a single object
you have to arrange [AAAA] B B C C C C C
so that B are not together

one method is
arrange [AAAA] and the 5 C's first
e.g * [AAAA] * C * C * C * C * C *
this creates 7 places (marked *) for the B's.
hence number of arrangements is found

another method is
find number of arrangements when B's are together, i.e of [AAAA] [BB] C C C C C
subtract from no restrictions on B's & A's together
0
1 week ago
#4
(Original post by mygjjgknj)
I have one question. I saw in the examiner report that an error is to arrange AAAA and multiply with 4! . How come AAAA doesn't have to be arranged? Is it because they are identical?
If the 4! is refering to the A's, then yes: Since you cannot distinguish between the individual A's there is only one possible arrangement of them.
#5
I see, thank you!
(Original post by ghostwalker)
If the 4! is refering to the A's, then yes: Since you cannot distinguish between the individual A's there is only one possible arrangement of them.
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Solent University
Mon, 25 Mar '19
• Cardiff University
Wed, 27 Mar '19
• University of Portsmouth
Wed, 27 Mar '19

### Poll

Join the discussion

#### Where do you need more help?

Which Uni should I go to? (149)
18.53%
How successful will I become if I take my planned subjects? (79)
9.83%
How happy will I be if I take this career? (136)
16.92%
How do I achieve my dream Uni placement? (114)
14.18%
What should I study to achieve my dream career? (79)
9.83%
How can I be the best version of myself? (247)
30.72%