A teacher has 30 students in a classroom. She has 6 seats in the front row. How many ways can she arrange her students to sit in the front row?

427,518,000  ways.

Step-by-step explanation:

-This is a permutation problem of the form:

Where n is the number of objects and r is the number of objects taken at a time.

-Permutation is a linear order or sequence arrangement of a set's elements.

-The number of ways can therefore be calculated as:

Hence, the 30 students can be arranged in 427,518,000 different ways.

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.