Binomial

Pascal's Triangle

... down to N=10.

TableForm[Table[Binomial[n, k], {n, 0, 10}, {k, 0, n}]]

Binomial coefficients

Again for N=20.  The "Table" function in Mathematica makes a list, looping over i from 0 to 20.

b20  =  Table[Binomial[20, i], {i, 0, 20}]

Type Options[BarChart] to see the various custom settings you can use to change what this next picture looks like.  
We need to load the Graphics`Graphics` package to turn on the BarChart stuff, first.

<< Graphics`Graphics`;

BarChart[b20,  BarLabels ->  Range[0, 20] ]

Binomial Probability Distribution, N=20, p=0.2

p = 0.2;
q = 1 - p;
probability  =  
      Table[    Binomial[20, i] (p^i) 
          (q^((20 - i)))      ,  {i, 0, 20}]

These values are the probability of getting exactly msuccesses in 20 trials, where the probability of success p = 0.2, for m=0,1,2,...,20.

{probability, Range[0, 20]} // TableForm

And here are the cumulative probabilities, which you get by adding the numbers in the previous list from 0 up to i.  This gives the probability of 0 to m successes in 20 trials, again with p = 0.2.

cumulative  =  
      Table[ Total[probability[[Range[i + 1]]]],  {i, 0, 
          20}]

p1  = 
        ListPlot[probability,  PlotJoined -> True,  
          PlotStyle -> Hue[ .6]];
p2  =  
        ListPlot[cumulative,  PlotJoined -> True,  
          PlotStyle -> Hue[ .3]];
Show[p1, p2,  AxesLabel -> {"m", "probability"}, 
      PlotLabel -> "N=20, p=0.2"]

Here's what a simple bar chart in Mathematica look like.

<< Graphics`Graphics`;
BarChart[{1, 6, 15, 20, 15, 6, 1}]