That's Just Math

A House Divided

Atomic Chess

Dots on a Line

Three tails

Password Fail

Free throws

Flappy Bird

Chance of Rain

A House Divided

What is the chance that a family with 10 kids will have 5 boys and 5 girls?

There are 2^10 = 1024 possible combinations of boy/girl children. For each child born, it is either a girl or a boy (thus the 2). We repeat this 10 times to give us the ^10 exponent. Girl-boy-boy-girl-boy-girl-girl-girl-boy-boy is one such combination that will give us 5 boys and 5 girls.

There are "10 choose 5" many of these combinations. That is, we need to choose 5 of the 10 children to be girls and the remaining 5 will be boys.

10 choose 5 can be calculated as 10!/((10-5)!*5!) = 10*9*8*7*6 = (5*4*3*2*1) = 252

So we have 252 out of the 1024 possibilities that result in 5 girls and 5 boys, or 24.6%.

Atomic Chess

What is the chance that a family with 10 kids will have 5 boys and 5 girls?

There are 2^10 = 1024 possible combinations of boy/girl children. For each child born, it is either a girl or a boy (thus the 2). We repeat this 10 times to give us the ^10 exponent. Girl-boy-boy-girl-boy-girl-girl-girl-boy-boy is one such combination that will give us 5 boys and 5 girls.

There are "10 choose 5" many of these combinations. That is, we need to choose 5 of the 10 children to be girls and the remaining 5 will be boys.

10 choose 5 can be calculated as 10!/((10-5)!*5!) = 10*9*8*7*6 = (5*4*3*2*1) = 252

So we have 252 out of the 1024 possibilities that result in 5 girls and 5 boys, or 24.6%.

A House Divided

What is the chance that a family with 10 kids will have 5 boys and 5 girls?

There are 2^10 = 1024 possible combinations of boy/girl children. For each child born, it is either a girl or a boy (thus the 2). We repeat this 10 times to give us the ^10 exponent. Girl-boy-boy-girl-boy-girl-girl-girl-boy-boy is one such combination that will give us 5 boys and 5 girls.

There are "10 choose 5" many of these combinations. That is, we need to choose 5 of the 10 children to be girls and the remaining 5 will be boys.

10 choose 5 can be calculated as 10!/((10-5)!*5!) = 10*9*8*7*6 = (5*4*3*2*1) = 252

So we have 252 out of the 1024 possibilities that result in 5 girls and 5 boys, or 24.6%.

A House Divided

What is the chance that a family with 10 kids will have 5 boys and 5 girls?

There are 2^10 = 1024 possible combinations of boy/girl children. For each child born, it is either a girl or a boy (thus the 2). We repeat this 10 times to give us the ^10 exponent. Girl-boy-boy-girl-boy-girl-girl-girl-boy-boy is one such combination that will give us 5 boys and 5 girls.

There are "10 choose 5" many of these combinations. That is, we need to choose 5 of the 10 children to be girls and the remaining 5 will be boys.

10 choose 5 can be calculated as 10!/((10-5)!*5!) = 10*9*8*7*6 = (5*4*3*2*1) = 252

So we have 252 out of the 1024 possibilities that result in 5 girls and 5 boys, or 24.6%.