Puzzle:A woman has seven cookies--four chocolate chip and three peanut butter. She gives one cookie to each of her six children: Nick, Ron, Kim, Deb, Max, and Terrall. If Deb will only eat the kind of cookie that Kim eats, in how many different ways can the cookies be distributed?
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Solution: There are two possibilities in this problem. Either Kim and Deb will both get chocolate chip cookies or Kim and Deb will both get oatmeal cookies.If Kim and Deb both get chocolate chip cookies, then there are 3 oatmeal cookies and 2 chocolate chip cookies left for the remaining four children.
There are 5!/3!2!=10ways for these remaining cookies to be distributed--four of the cookies will go to the children. (There are 5! ways to arrange 5 objects but the three oatmeal cookies are identical so we divide by 3!, and the two chocolate chip cookies are identical so we divide by 2!.)\
If Kim and Deb both get oatmeal cookies, there are 4 chocolate chip cookies and 1 oatmeal cookie left for the remaining four children.There are 5!/4! = 5 ways for these 5 remaining cookies to be distributed--four of the cookies will go to the children, one to the dog.(There are 5! ways to arrange 5 objects but the four chocolate chip cookies are identical so we divide by 4!.)
Accounting for both possibilities, there are 10 + 5 = 15 ways for the cookies to be distributed.
Winner: Austin
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ReplyDeleteOn another note, what is the woman going to do with the last cookie? Are the cookies "special"? I know once I had these special cookies and they transformed me into this super being that could like eat like anything in sight and then I would poop out this amazing gold brick that I would distribute to the poor and then I would have x ray eyes and i could see what people were doing inside there houses while flying around and I also had like super strength to lift like buildings and stuff... and then there was this monster that went like totally ballistic mad and then I was like "no way man, this is like totally my town" and like I took care of it when it took a smell of by breath and like I totally got like the key to the city and like the people were like "hooraayyy!!"
ON SECOND THOUGHT IT'S 4
ReplyDeletethe person who answers the question correctly will get the remaining cookie.
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