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# Find the number of ways to arrange the letters A, B, B, C, C, C. (Both B's are identical, and all three C's are identical.)

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Find the number of ways to arrange the letters A, B, B, C, C, C. (Both B's are identical, and all three C's are identical.)

and

Alison has five different hats, six different bracelets, and seven cats. She wants to take a selfie with a hat, a bracelet, and two cats. How many different selfies can she take?

Can someone please explain to me these problems?

Mar 5, 2019

#1
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1. 2 B's and 2 C's repeat, so the total number of possible ways to arrange it is $$\frac{6!}{2!*3!}=\boxed{60}.$$

2. I think the answer is $$\binom{5}{1}*\binom{6}{1}*\binom{7}{2}=\boxed{630}.$$

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Mar 5, 2019
edited by tertre  Mar 5, 2019
edited by tertre  Mar 5, 2019
#2
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For some reason it says that #1 is wrong?

Guest Mar 5, 2019
#3
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Tertre probably just made a typo...it should be

6! / (2! * 3! ) =    720 / (2 * 6)  =  720 / 12  =    60  ways

CPhill  Mar 5, 2019
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Yes, thank you!

tertre  Mar 5, 2019
#5
+98168
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No prob....easy to make mistakes on here.....

CPhill  Mar 5, 2019