August 21st, 2009, 08:51 AM  #1 
Newbie Joined: Aug 2009 Posts: 2 Thanks: 0  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? 
August 22nd, 2009, 03:57 PM  #2 
Member Joined: Jul 2009 Posts: 34 Thanks: 0  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)

September 14th, 2009, 05:41 AM  #3  
Newbie Joined: May 2009 Posts: 25 Thanks: 0  Re: Permutation pblm Quote:
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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