In a family of 5 children, how many different ways can you have 3 boys and 2 girls?
You can have...1 boy then a girl then a boy then a girl then a boy yeah I don't know but it's god to guess in life
good*
I assume you are asking about their birth order. Otherwise, there is only one way to have 3 boys and 2 girls: have 3 boys and 2 girls!
5!/(3!2!) = 10
To calculate the number of different ways you can have 3 boys and 2 girls in a family of 5 children, you can use combinations.
First, let's consider the positions of the boys and girls. Out of the 5 positions, we need to choose 3 for the boys and 2 for the girls.
To calculate the number of ways to choose a certain number of objects from a larger set, we use the combination formula, which is denoted as "nCr," where n is the total number of objects to choose from, and r is the number of objects to be chosen. The formula for combinations is:
nCr = n! / (r!(n-r)!)
In our case, n = 5 (total number of children) and r = 3 (number of boys). Therefore, the number of combinations of boys is:
5C3 = 5! / (3!(5-3)!) = (5! / (3!2!)) = (5 × 4 × 3!) / (3! × 2 × 1) = (5 × 4) / (2 × 1) = 10
Next, we need to consider the number of ways the girls can occupy the remaining 2 positions. Similarly, we can calculate the number of combinations for the girls:
2C2 = 2! / (2!(2-2)!) = 2! / (2!0!) = 1
To find the overall number of different ways to have 3 boys and 2 girls, we multiply the number of combinations for boys (10) by the number of combinations for girls (1):
10 × 1 = 10
Therefore, there are 10 different ways to have 3 boys and 2 girls in a family of 5 children.