How many distinct permutations can be formed using the letters of the word prepared

5,040

Step-by-step explanation:

Hmmm...this one is a bit tricky. First, prepared contains 8 letters. To find the number of ways this can be rearranged use the fundamental counting principle.

First letter - 8 choices

Second letter - 7 choices

Third letter - 6 choices

So the number of outcomes would be

But wait, there's more. Prepared has some duplicate letters, the P, R, and E. That means if the letters were written ppeerrad it would be indistinguishable if it was the first or second P written first. So that means the letter P generates 2 outcomes that appear the same

Same for the letter R

And same for the letter E

∠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.