Question

In how many ways 6 students and 4 teachers be arranged in a row so that no two teachers are together

Answer 1

See the attach file for ans

Answer 2

Answer:

604800 ways 6 students and 4 teachers be arranged in a row so that no two teachers are together.  

Step-by-step explanation:

To find : In how many ways 6 students and 4 teachers be arranged in a row so that no two teachers are together?

Solution :

First we consider the positions of the teachers and students.

there are 4 teacher positions with 3 students inserted between to keep the teachers apart.

We have 3 students and 4 teachers that can separate them.

There are 7 positions to deal with 3 of those are students.

So we get 7 choose 3.

The teachers can be ordered 4! ways and the students can be ordered 6! ways.

Required ways are $^7C_3\times 4!\times 6!$

$=\frac{7!}{3!(7-3)!}\times 4!\times 6!$

$=\frac{7\times 6\times 5\times 4!}{3\times 2\times 4!}\times 4\times 3\times 2\times 6\times 5\times 4\times 3\times 2$

$=7\times 5\times 4\times 3\times 2\times 6\times 5\times 4\times 3\times 2$

$=604800$

Therefore, 604800 ways 6 students and 4 teachers be arranged in a row so that no two teachers are together.