Hello, i'm having a trouble in solving the following questions. Please help me.1. In how many ways, four letters can be put in four envelopes so that no letter gets it's perfect match?2. how namy triangles can be formed in a n-sided polygon where no side of the triangle is the side of the polygon?

1)Probability of putting first letter in correct envelope: 1/4

Probability of putting second letter in wrong envelope: 2/3

Probability of putting third letter in wrong envelope: 1/2

Probability of putting last letter in wrong envelope: 1/1

Multiply all those together and you get 1/12. We have four envelopes, so (1/12)*4 = 1/3.

2. the total number of triangles having no side common with polygon = ⁿc_{3 ^–}n× ^(n-4) c₁ - n