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# Help!

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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
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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