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1) Everyone at the party shook hands with everyone else exactly once. If there were a total of 21 handshakes, how many people were at the party?

 

2) Kathy tossed a coin 8 times and got 3 heads and 5 tails. How many different sequences of results could she have gotten? 

 

Thanks! These are a couple problems that have stumped me and need some help on :)

 May 4, 2019
 #1
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1. We can use the handshakes formula here...n(n-1) / 2 =21 n(n-1)=42, n=7 people at the party.

 

2. Think of arranging three identical letters with five other identical letters. How many ways are there to do this?

 May 4, 2019
 #2
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Thanks!

 May 4, 2019
 #3
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No problem...and the answer to the second question should be \(\frac{8!}{3!*5!}=\boxed{56}\) different sequences.

tertre  May 4, 2019

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