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I am really stuck on this

 

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

 Jun 3, 2023
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1 - The first child has 6 choices

 

2 - The sibling of the first child has 5 - 1=4 choices [since he/she cannot sit directly in front of his /her sibling]

 

3 - The first sibling of the 2nd pair has 4 choices.

 

4 - His/her sibling has 3- 1 =2 choices [Same reason as in 2 above]

 

5 - The first sibling of the 3rd pair and his /her sibling have the remaining 2 chairs.

 

6 - The total number of ways of seating the 3 pairs of siblings=6 x 4 x 4 x 2 x 2 x 1 =384 ways.

 Jun 4, 2023

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