Counting Examples ¶

Ordered distribution With Replacement Example ¶

How many words can we create with the letters of Mississippi?

• we got 1 M ($o_1$)
• we got 4 I ($o_2$)
• we got 4 S ($o_3$)
• we got 2 P ($o_4$)
• we got 11 letters

@ \frac{11!}{1! * 4! * 4! * 2!} = 34650 @

Unordered Sampling With Replacement Example ¶

If we have $n=2$ and a set $[1,5,7]$. We have $k=3$ and:

@ C^{3-1}_{2+3-1} = 6 @

It means that we have 6 combinations:

• $\lbrace1,5\rbrace$ (e.g., $(1,5)\ \text{and}\ (5,1)$)
• $\lbrace1,7\rbrace$ (e.g., $(1,7)\ \text{and}\ (7,1)$)
• $\lbrace5,7\rbrace$ (e.g., $(5,7)\ \text{and}\ (7,5)$)