How many ways can 10 students be seated in a row?

Answer:- 1

Explanation:-

Solution:

5 students can be seated out of 10 students in 10C5 ways . Remaining 5 will be seated in,

= 5C5 ways .

Students of each row can be arranged as, = 5! *5! ways. Two sets of paper can be arranged themselves in, = 2! ways. Thus, Total arrangement,

= 10C5 * 5! *5! *2

= 7257600.

in a row, means there are not seating in a circular seats

but instead, on a straight row of seats

if two students insists to sit beside each other

therefore, the two seat they will occupied will be count as one

so, we have 5 - 1 = 4 seats

P(10, 4)

= 10!/(10 - 4)!

= 10!/6!

= 5040 ways

now, we can arrange the two who insists on sitting together.

2! = 2

multiply the answers

5040*2

= 10,080 ways

120 ways is the correct answer

$\begingroup$

What I'm thinking: Find total ways that the ten people can be seated, which is 10!.

Then I take that number and subtract the ways the these two people would be seated next to each other. I do this by treating these two people as a single space, which leaves the eight other students plus that space consisting of the two. This would mean 9!

Then, 10! - 9! = 3265920 ways for the ten people to be seated so that a certain to are not next to each other.