How many arrangements of balloons can be made using three red, four white, and five gold balloons?
(3+4+5)! / (3!4!5!) = 27,720
To calculate the number of arrangements of balloons, you can use the concept of permutations. The total number of balloons is the sum of the individual colors: 3 red + 4 white + 5 gold = 12 balloons.
The formula for finding the number of arrangements is given by n!, where n is the total number of objects (balloons) and "!" denotes factorial.
Therefore, the number of arrangements can be calculated as follows:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600.
So, there are 479,001,600 possible arrangements of three red, four white, and five gold balloons.
To determine the number of arrangements of the balloons, you can use the concept of permutations.
Permutations are used when order matters. In this case, the order of the balloons in each arrangement is important.
To calculate the number of arrangements, you can multiply the number of choices for each color.
Step 1: Count the number of red, white, and gold balloons available:
- Red balloons: 3
- White balloons: 4
- Gold balloons: 5
Step 2: Determine the number of choices for each color:
- For the red balloons, you have 3 choices.
- For the white balloons, you have 4 choices.
- For the gold balloons, you have 5 choices.
Step 3: Multiply the number of choices for each color:
Number of arrangements = (Number of choices for red balloons) * (Number of choices for white balloons) * (Number of choices for gold balloons)
Number of arrangements = 3 * 4 * 5
Number of arrangements = 60
Therefore, there are 60 different arrangements of the three red, four white, and five gold balloons.