There are 20 red, 20 green and 20 blue balls in an urn. In how many different ways can 10 balls be selected?
How many ways are there if there are 6 red balls instead of 20?
To solve this problem, we can use the concept of combinations.
For the first part of the question, where there are 20 red, 20 green, and 20 blue balls in the urn, we need to find the number of ways to select 10 balls.
We can approach this by considering all the possible combinations of balls that can be chosen. Since we need to select 10 balls out of a total of 60 (20 red + 20 green + 20 blue), we can use the formula for combinations:
nCr = n! / (r!(n-r)!)
Where n is the total number of balls and r is the number of balls to be selected.
In this case, the formula becomes:
60C10 = 60! / (10!(60-10)!)
= 60! / (10!50!)
= (60 * 59 * 58 * ... * 51) / (10 * 9 * 8 * ... * 1)
To calculate this value, you can use a calculator or a computer program capable of performing large factorial calculations.
For the second part of the question, where there are 6 red balls instead of 20, we can follow the same approach. Now we have a total of 46 balls (6 red + 20 green + 20 blue) and need to select 10.
Using the formula for combinations:
46C10 = 46! / (10!(46-10)!)
= 46! / (10!36!)
= (46 * 45 * 44 * ... * 37) / (10 * 9 * 8 * ... * 1)
Again, you can use a calculator or a computer program to calculate this value.
By comparing the results of the two calculations, you can determine the different ways to select 10 balls in each scenario.