There are 1,207,084,032,000 ways for 6 CE majors and 10 CS majors to stand next to each other in the lines.
We use permutations and combinations for solving this problem. We fix the position of CS students so that they can stand in a fixed place by
= 10! ways (i)
Now, there are 11 places left for CE students so that no two CE students stand next to each other.
6 CE students in the rest of the 11 places can sit by = 11! / (11-6)! ways (ii)
Hence, using the values of (i) and (ii), we get -
= (10! * 11!) / (11-6)!
= 1,207,084,032,000
Therefore, we have 1,207,084,032,000 ways in which the six CE majors and ten CS majors can stand in a line so that no two CE majors stand next to each other.
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