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?

3. There are 16 teams in a basketball league. Eight teams are in the East conference, and the other eight teams are in the West conference. If a team plays each other team from the same conference 4 times and from the difference conference twice, how many games are there in total?

sudsw12 Apr 13, 2019

#1**+1 **

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?

There were 7 people

The 7th person shakes 6 hands

The 6th ,5 hands

The 5th, 4 hands

.

.

.

The 2nd,1 hand

The last...0 hands (everyone else has shaken this person's hand once)

So

6 + 5 + 4 + 3 + 2 + 1 + 0 = 21

CPhill Apr 13, 2019

#2**+1 **

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

This is the same as finding the number of identifiable "words" that can be formed from the "word" HHHTTTTT

We have

8!

____ = 56 identifiable "words" or sequences

3! 5!

CPhill Apr 13, 2019

#3**+1 **

3. There are 16 teams in a basketball league. Eight teams are in the East conference, and the other eight teams are in the West conference. If a team plays each other team from the same conference 4 times and from the difference conference twice, how many games are there in total?

Never sure about these....but....here's my best attempt

Suppose that each team plays every other team in its conference once and every other team in the other conference once

Within one conference......it will be similar to the "handshake" problem

There will be (8*7)/2 = 28 games withiin each conference if each team plays each other once

So....the total number of intra-coference games will be four times this = 4 (28 + 28) = 4(56) = 224 games

If each team plays each team from the other conference once there will be (8)(8) = 64 games

But....we must double this = 128 games

So....the total number of games = 224 + 128 = 352 games

CPhill Apr 13, 2019