Hi All,

We're asked to arrange a group of 3 adults and 4 children in 7 seats with adults in the first, third, and seventh seats. We're asked for the number of arrangements possible. This question is a variation on a standard Permutation question. To solve it, we have to go from space to space and keep track of the 'options' available for each (noting that once we place a person, there is one fewer person available for the next equivalent spot).

For the 1st spot, there are 3 options

For the 2nd spot, there are 4 options

For the 3rd spot, there are 2 options

For the 4th spot, there are 3 options

For the 5th spot, there are 2 options

For the 6th spot, there are 1 options

For the 7th spot, there are 1 options

Total arrangements = (3)(4)(2)(3)(2)(1)(1) = 144 possible arrangments

Final Answer:

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