Question

A box contains 5 red balls, 7 green balls and 6 yellow balls . In how many ways can 6balls be chosen if there should be 2 balls of each color?

Answer 1

5C2 * 7C2 * 6C2

Answer 2

Help

Answer 3

School

Answer 4

[AI-generated answer — Explain Bot]

To find the number of ways to choose 6 balls with 2 balls of each color, we can break down the problem into three steps:

Step 1: Choose 2 red balls from the 5 available.
Step 2: Choose 2 green balls from the 7 available.
Step 3: Choose 2 yellow balls from the 6 available.

To find the number of ways to choose 2 balls of a specific color from a certain number of balls of that color, we use the combination formula:

nCr = n! / (r! * (n-r)!),

where n is the total number of balls of that color and r is the number of balls to be chosen.

Step 1: n1C2 = 5C2 = 5! / (2! * (5-2)!) = 10.
Step 2: n2C2 = 7C2 = 7! / (2! * (7-2)!) = 21.
Step 3: n3C2 = 6C2 = 6! / (2! * (6-2)!) = 15.

To find the total number of ways to choose 6 balls with 2 balls of each color, we multiply the results from each step:

Total number of ways = Step 1 * Step 2 * Step 3 = 10 * 21 * 15 = 3,150.

Therefore, there are 3,150 ways to choose 6 balls with 2 balls of each color from the given box.