Which figure will tessellate the plane? A. regular pentagon B. regular decagon C. regular octagon D. regular hexagon

D. regular hexagon

A hexagon is composed of 6 congruent equilateral triangles. Each equilateral triangle has interior angle of 60 degrees. Adding 6 such angles together gets you to 360 degrees. So we've done one full rotation and covered every bit of the plane surrounding a given point. Extend this out and you'll be able to cover the plane. A similar situation happens with rectangles as well (think of a grid, or think of tiles on the wall or floor)

In contrast, a regular pentagon has interior angle 108 degrees. This is not a factor of 360, so there is no way to place regular pentagons to have them line up and not be a gap or overlap. This is why regular pentagons do not tessellate the plane. The same can be aside about decagons and octagons as well.

The number of ways to select 4 digits from 10  digits is
₁₀C₄ = 10!/(4!*6!) 
       = (10*9*8*7*6!)/(4*3*2*1*6!)
       = (10*9*8*7)/(4*3*2)
       = 210 

If order is not important, the number of arrangements of 6,7,8,9 in any order is
4! = 4*3*2*1
    = 24
The probability that these 4 digits are assigned is
24/210 = 0.1143