Question

Hello! I am really struggling with this question and it would be great to have some help!

Answer 1

Question:

How many ways can two teachers, four male students, five female students and one administrator be arranged if the teachers must sit together, the male students must sit together and the female students must sit together?

Step 1:

If the two teachers must sit together, they will be arranged in

`2!ways`

Step 2:

If the male students must sit together,they will be arranged in

`4!ways`

Step 3:

If the female students must sit together, they will be arranged in

`5!ways`

Step 4:

If they are to be arranged as a group along with the administrator, they will be arranged as

`4!ways`

Hence,

The number of ways in which they can be arranged will be given below as

`\begin{gathered} 2!*4!*5!*4! \\ =2*1*4*3*2*1*5*4*3*2*1*4*3*2*1 \\ =138240ways \end{gathered}`

Hence,

The final answer is

`\Rightarrow138240ways`