How to calculate this permutaion problem

Question

In how many ways can 3 teachers and 4 pupils be arranged in a line if the pupils and teachers must alternate? . how to get the answer? the ans :144

Answer 1

Let '|'-represent students and '*'-represent the gaps between them where you need to place the teachers for alternate configuration then:

            | * | * | * | 

So now you can permute the 4 students in 4! ways and on placing 3 teachers in the gap you can permute them in 3! ways

Therefore, No. of ways of arranging them in alternate position=3!*4!=6*24=144,which is your answer

Since it is 'and' segment so we are multiplying( 3 teachers and 4 pupils)

Answer 2

Hint: first, show that the pupils must be on the first, third, fifth and seventh places. Then, think about how many ways you can place the pupils on those $4$ places and how many ways you can place the teachers on the remaining. Are the two arrangements dependent on each other?