a box contains 5 red balls,7 green balls ,and 6 yellow ball.In how many ways can 6 balls be choosen if there should be 2 balls of each color
how many balls are there inside the box
=3,150
To find the number of ways to choose 6 balls with 2 balls of each color, we need to calculate the combinations.
First, we select 2 red balls out of the 5 available red balls. This can be calculated as C(5, 2) = 5! / (2! * (5-2)!) = 10 ways.
Next, we select 2 green balls out of the 7 available green balls. This can be calculated as C(7, 2) = 7! / (2! * (7-2)!) = 21 ways.
Finally, we select 2 yellow balls out of the 6 available yellow balls. This can be calculated as C(6, 2) = 6! / (2! * (6-2)!) = 15 ways.
To calculate the total number of ways, we multiply the number of ways for each color together: 10 * 21 * 15 = 3,150.
Therefore, there are 3,150 ways to choose 6 balls with 2 balls of each color.
To find the number of ways to choose 6 balls with 2 balls of each color, we can use a combination formula.
First, let's calculate the number of ways to choose 2 balls of each color:
For the red balls: C(5, 2) = 5! / (2! * (5-2)!) = 10 ways
For the green balls: C(7, 2) = 7! / (2! * (7-2)!) = 21 ways
For the yellow balls: C(6, 2) = 6! / (2! * (6-2)!) = 15 ways
Now, let's multiply the number of ways for each color together to find the total number of ways to choose 2 balls of each color:
Total ways = 10 * 21 * 15 = 3,150 ways
Therefore, there are 3,150 ways to choose 6 balls if there should be 2 balls of each color.