Tricky Indie Maths q
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Tricky Indie Maths q
Can anyone please help with the following question (no answers were provided!):
I have 3 types of cuddly toy on my bedroom shelf: a teddy, a giraffe and a panda.
a. How many different ways can I arrange them on my shelf?
b. If I buy another teddy identical to the first, how many different ways can I now arrange them?
I have no idea of how to find the correct answer except by laboriously drawing the possibilites- what is the best way to approach this kind of question?
Many thanks
I have 3 types of cuddly toy on my bedroom shelf: a teddy, a giraffe and a panda.
a. How many different ways can I arrange them on my shelf?
b. If I buy another teddy identical to the first, how many different ways can I now arrange them?
I have no idea of how to find the correct answer except by laboriously drawing the possibilites- what is the best way to approach this kind of question?
Many thanks
Re: Tricky Indie Maths q
I always say 'if in doubt, draw it out'.
With this type of question, writing out the different combinations of t,p,g doesn't take long but must be written out systematically rather than randomly.
a) tpg, tgp, ptg, pgt, gtp, gpt = 6 ways of ordering the toys
b) ttpg, ttgp, tptg, tgtg, tpgt, pttg, ptgt, pgtt, gttp, gtpt, gtpt, gptt= 12 ways
With this type of question, writing out the different combinations of t,p,g doesn't take long but must be written out systematically rather than randomly.
a) tpg, tgp, ptg, pgt, gtp, gpt = 6 ways of ordering the toys
b) ttpg, ttgp, tptg, tgtg, tpgt, pttg, ptgt, pgtt, gttp, gtpt, gtpt, gptt= 12 ways
Last edited by Blitz on Fri Oct 14, 2011 6:51 pm, edited 1 time in total.
Re: Tricky Indie Maths q
the first part of the question falls under the heading of Factorial...
if there are 3 items, then the answer is 3 factorial, i.e. 1x2x3=6
if there are 3 items, then the answer is 3 factorial, i.e. 1x2x3=6
Re: Tricky Indie Maths q
TGPI have 3 types of cuddly toy on my bedroom shelf: a teddy, a giraffe and a panda.
a. How many different ways can I arrange them on my shelf?
b. If I buy another teddy identical to the first, how many different ways can I now arrange them?
TPG
GTP
GPT
PTG
PGT
If you think about the three toys - any one can be put down first ie three choices. Then when that is done there are two choices for the second toy so 3 x 2 x 1
The second is more tricky - with four different toys it would be 4 x 3 x 2 x 1 but some of them look the same because the two bears are identical. If I call the teddies T you can see I get some duplicates:
TTGP
TTPG
TGTP
TGPT
TPTG
TPGT
TTGP duplicate
TTPG duplicate
GTTP
GTPT
PTTG
PTGT
TGTP duplicate
TPTG duplicate
GTTP duplicate
GPTT
PTTG duplicate
TGTP duplicate
TGPT duplicate
TPGT duplicate
GTPT dulicate
GPTT duplicate
PTGT duplicate
PGTT
ie 12 ways - the theory says (4 x 3 x 2 x 1) divided by (2 x 1) because two are identical and we can ignore these.
Last edited by Guest55 on Fri Oct 14, 2011 7:31 pm, edited 1 time in total.
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Re: Tricky Indie Maths q
Thank you for such quick replies- If in doubt draw it out sounds like a good maxim for DD to remember.
Guest 55- your explanation of why it would be 3 x 2 x 1 is perfect (DD agreed). I had forgotten about factorials from all those years ago.
DD was also very impressed that I had apparently instant access to Maths whizzes!
Guest 55- your explanation of why it would be 3 x 2 x 1 is perfect (DD agreed). I had forgotten about factorials from all those years ago.
DD was also very impressed that I had apparently instant access to Maths whizzes!
Re: Tricky Indie Maths q
I last did factorials when I was in school myself back in the early eighties..
Re: Tricky Indie Maths q
When teaching this I always do the explanantion before introducing the idea that e.g. 9! is a lot easier to write than 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1