How Many Ways To Group Babies: A Combination Pattern Explained

To determine the pattern, we need to analyze the given information.

In the first scenario, we are told that there are 4 babies and 2 of them are girls. This means that we have 2 boys and 2 girls.

The possible ways of grouping the babies are as follows:

1. Boy, Boy, Girl, Girl
2. Boy, Girl, Boy, Girl
3. Boy, Girl, Girl, Boy
4. Girl, Boy, Boy, Girl
5. Girl, Boy, Girl, Boy
6. Girl, Girl, Boy, Boy

So, there are 6 possible ways of grouping the babies when there are 4 babies and 2 of them are girls.

Now, let's analyze the second scenario. We are told that there are 5 babies and 2 of them are girls. This means that we have 3 boys and 2 girls.

The possible ways of grouping the babies can be calculated using combinations. We can choose 2 positions out of the 5 positions to place the girls, and the remaining 3 positions will be for the boys. The formula for combinations is nCr = n! / (r!(n-r)!).

So, the possible ways of grouping the babies when there are 5 babies and 2 of them are girls can be calculated as follows: 5C2 = 5! / (2!(5-2)!) = 10

We can apply the same logic to the third scenario when there are 10 babies and 2 of them are girls: 10C2 = 10! / (2!(10-2)!) = 45

Therefore, the pattern is as follows:

• When there are 4 babies and 2 of them are girls, there are 6 possible ways of grouping.
• When there are 5 babies and 2 of them are girls, there are 10 possible ways of grouping.
• When there are 10 babies and 2 of them are girls, there are 45 possible ways of grouping.

The pattern seems to follow a combination calculation, where the number of ways of grouping is equal to the combination of choosing 2 positions for the girls out of the total number of positions (number of babies).