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August 21st, 2009, 08:51 AM   #1
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Permutation pblm

Can someone help with this question on perms & combinination , I cannot sort the second one?


An artist has 6 water color paintings and 4 oil paintings . She wishes to select 4 out of these 10 paintings .
(1) Find the number of different selections she can make
(2) In how many ways of these selections will there be more watercolor paintings than oil paintings?
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August 22nd, 2009, 03:57 PM   #2
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Re: Permutation pblm

The second one is just: (ways to take 3 water colour paintings and 1 oil painting) + (ways to take 4 water colour paintings)
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September 14th, 2009, 05:41 AM   #3
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Re: Permutation pblm

Quote:
Originally Posted by rdev
Can someone help with this question on perms & combinination , I cannot sort the second one?


An artist has 6 water color paintings and 4 oil paintings . She wishes to select 4 out of these 10 paintings .
(1) Find the number of different selections she can make
(2) In how many ways of these selections will there be more watercolor paintings than oil paintings?
First off define where all the water colours and oils are identical - and whether order of selection matters.

Case 1) All paintings are different and order within the selection doesnt matter.
Answer is 10!/6!4! =210
Case 2) All paintings are different and order does matter
Answer is 10!/6! = 5040
Case 3) All oils and waters are identical and order doesn't matter.
Answer is 5 (either 4 oils, 3 oils, 2 oils, 1 oil or 0 oils in your selection of 4)

Case 4) All oils and waters are identical and order does matter.
Answer = 2^4 = 16
There is 1 way of selecting 4 oils. O,O,O,O
There are 4 ways of selecting 3 oils and 1 water. W,O,O,O
There are 6 ways of selecting 2 oils and 2 waters. W,W,O,O
There are 4 ways of selecting 1 oils and 3 water. W,O,O,O
There is 1 way of selecting 4 water.

I'm going to assume case 1)
In which case the problem becomes

How many ways can you select 4 waters from 6 waters. PLUS how many ways can you select 3 waters from 6 waters x how many ways can you select 1 oil from 4 oils.

= 6C2 + 6C3 x 4C1
= 15 + 80 = 95 out of the 210 possible selections.


Should the title of the problem refer to combinations rather than combinations ?
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