when a group photograph is taken, all the seven teachers should be in the

Solution:

For the first row:

There are 7 teachers in which the position of principal is fixed.

Therefore, the teachers can be arranged in $\mathrm{p}(7,7)=5040$.

For the second row:

The tallest students are at the ends and can be arranged in $2 !=2$ ways.

Rest 18 students can be arranged in $\mathrm{P}(18,18)$ ways.

Formula:

Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is

$P(n, r)=n ! /(n-r) !$

Therefore, permutation of 18 different objects in 18 places is

$P(18,18)=\frac{18 !}{(18-18) !}$

$=\frac{18 !}{0 !}=\frac{18 !}{1}=18 !$

Therefore, a total number of arrangements of the second row is $2 \times 18 !$

Total arrangements $=2 \times 18 ! \times 5040=10080 \times 18 !$

The total number of arrangements is $10080 \times 18 !$