Combinatorics and Graphs

In a company of 8 some people know each other, some don’t. They know the following number of people: 1, 1, 2, 2, 3, 4, 5, 6. (Acquaintances are mutual.) How many more connections (also mutual) must be made so that everybody will know everybody else?

• 4

• 16

• 32

• none of these answers

The graph above shows the matches already played in a chess tournament. How many more matches will be played if everybody has to play against all the other players once?

• 10

• 20

• 5

• none of these answers

There are 6 exercises on a maths practice worksheet. You can solve them in any order. In how many different orders can you solve the exercises if you want to solve all of them?

• 36

• 360

• 720

• 46656

• none of these

There are 6 exercises on a maths practice worksheet. You can solve them in any order. In how many different orders can you solve the exercises if you want to solve the two easiest exercises first and then all the rest?

• 720

• 48

• 24

• 360

• none of these

How many 4-digit even integers can be made from the digits 3, 4, 5, 6, 7, 8 if all the digits must be different?

• 720

• 360

• 24

• none of these

How many 4-digit even integers can be made from the digits 3, 4, 5, 6, 7, 8 if the digits don't have to be different?

• 4096

• 720

• 360

• 1296

• none of these

There are 15 students in a group, 7 boys and 8 girls. The teacher wants to choose 3 of them to act out a situation. In how many ways can she do this if the gender of the students does not matter?

• 2730

• 3375

• 455

• none of these

There are 15 students in a group, 7 boys and 8 girls. The teacher wants to choose 3 of them to act out a situation. In how many ways can she do this if there are two female roles and one male role?

• 196

• 448

• 168

• 392

• none of these

In a group of 18 people everybody shook hands eówith everybody else. How many handshakes were there?

• 306

• 162

• 153

• none of these

Tags

CCSS.HSF.BF.A.2

In a graph of 6 nodes the degrees of the nodes are the following: A(3), B(4), C(1), D(4), E(2). Which could be the degree of F?

• 1

• 2

• 3

• 5