Το καλάθι σου είναι άδειο.
COMBINATORICS I
{{exercise_number}}.
- Choose two plane figures of different colours in any order from the following set of items. Draw the chosen plane figures in the rectangle.
Chosen items:
- Fill in the table with your chosen plane figures. Find all the other possibilities. Draw them in the table as well. In how many different ways can you choose two figures of different colours from the set of items above?
The total number of possibilities is: 9
- Choose two items that are different in both colour and shape. Fill in the table with your chosen figures. Find all the other possibilities. Draw them in the correct cells of the table.
The total number of possibilities is: 6
- How does the number of possibilities change if you can choose two items only from the three blue plane figures? Draw your chosen figures. Find all the other possibilities. Draw them as well.
The total number of possibilities is: 3
Chosen items:
{{exercise_number}}. How many different initials can be written using the letters A, B and C if the letters can be repeated in an initial? The initials of Alan Brown are A. B.
- Fill in the table.
The total number of possibilities is: 9
- How many different initials can be written if the letters cannot be repeated?
The total number of possibilities is: 6
A
A
B
C
B
C
A.A.
{{exercise_number}}.
The children are playing a game in which one player is the hunter and another is the rabbit. Dave, Tom, Harriet and Katie all volunteered to play these roles. How many different ways can the rabbit and the hunter be chosen from them? Act it out. If Dave is the hunter, then Tom, Harriet or Katie can be the rabbit. Fill in the images with the possible outcomes based on the example.
D
T
H
K
H
The total number of possibilities is: 12
- How many different outcomes would there be if only a boy could be the hunter and only a girl could be the rabbit? Act it out as well.
The total number of possibilities is: 4
{{exercise_number}}.
- A box contains five marbles: two green, two blue and one red , all the same size. How many different ways can you take three marbles out of the box one by one, without putting any of them back?
If you take a green marble out first, you will take either a green, blue, or red marble out next. If the second marble you take out is also green, then the third marble will be either blue or red .
Complete the drawing.
Draw every possible solution in your notebook.
The total number of possibilities is:7
Draw every possible solution in your notebook.
The total number of possibilities is:
- How many different combinations are there if you take the three marbles out at once, and the order doesn't matter? Continue the drawing.
The total number of possibilities is: 5
{{exercise_number}}.
- Blair has homework in four subjects: math, English, French, and history.
If she starts with her math homework, how many different orders can she complete all her homework in? Draw a diagram to show all the possible orders.
The total number of possibilities is: 6
- How does the number of possibilities change if she can start with any of the four subjects?
The total number of possibilities is: 24
{{exercise_number}}. The third graders visited a botanical garden. From the entrance, three different paths led to the lake, from which two paths led to the palm house. How many different paths could the children take to reach the palm house from the entrance? Mark each possible route with a different colour on the image.
entrance
lake
palm house
The total number of possibilities is: 6
{{exercise_number}}. Every day after school, Frank goes to his grandmother's house for lunch and then heads home. There are four different routes from the school to his grandmother's house, and three different routes from his grandmother's house to his home. For how many days can Frank follow a different route? Draw all the possible paths using different colours on the map.
school
grandma's
place
place
home
The total number of possibilities is: 12
{{exercise_number}}. The third-graders learned how to read a map. They discovered that they can travel from their hometown to the county town either by bus or by car. From the county town, they can continue their journey to the capital by bus, car, or train. In how many different ways can they travel from their hometown to the capital? Complete the image below by drawing all the possible options
The total number of possibilities is: 6