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I believe all you have to do for this problem is take the total number of ways to permute the 26 letters of the alphabet | I believe all you have to do for this problem is take the total number of ways to permute the 26 letters of the alphabet | ||
, which is 26!, and subtract all of the strings which contain the words 'fish', 'cat', and 'bird'. Namely if A='fish', B='cat', and C='bird' - |A or B or C| = |A| + |B| + |C| - |A and B| - |A and C| - |B and C| + |A and B and C|.--[[User:Spfeifer|Spfeifer]] 19:06, 27 January 2009 (UTC) | , which is 26!, and subtract all of the strings which contain the words 'fish', 'cat', and 'bird'. Namely if A='fish', B='cat', and C='bird' - |A or B or C| = |A| + |B| + |C| - |A and B| - |A and C| - |B and C| + |A and B and C|.--[[User:Spfeifer|Spfeifer]] 19:06, 27 January 2009 (UTC) | ||
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| + | However, if I understand the question correctly, each letter is only getting used once, so if 'i' is being used to make 'fish', it can't also be used to make bird. Same with 'r' for rat and bird. I'm i correct in thinking this? If so, using the notation from above, |A and C| and |B and C| should both be 0, correct? | ||
Revision as of 14:13, 27 January 2009
Ok does anyone know how to go about this problem?
I believe all you have to do for this problem is take the total number of ways to permute the 26 letters of the alphabet , which is 26!, and subtract all of the strings which contain the words 'fish', 'cat', and 'bird'. Namely if A='fish', B='cat', and C='bird' - |A or B or C| = |A| + |B| + |C| - |A and B| - |A and C| - |B and C| + |A and B and C|.--Spfeifer 19:06, 27 January 2009 (UTC)
However, if I understand the question correctly, each letter is only getting used once, so if 'i' is being used to make 'fish', it can't also be used to make bird. Same with 'r' for rat and bird. I'm i correct in thinking this? If so, using the notation from above, |A and C| and |B and C| should both be 0, correct?
