In how many ways can we seat 3 pairs of siblings in a row of 7 chairs, so that nobody sits next to their sibling

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as ∩∩

By set theory, we have;

= =  

=

Therefore;

Where;

= The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

= The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

= The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

= The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

= The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

= The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

= The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

= The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

= 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

= 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as  = 1,968

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (

i think it is 18

step-by-step explanation: