Question

use Pascal's triangle to find the number of ways to choose 4 shirts from 6 shirts

Answer 1

You mean
\[{6 \choose 4}\]?

Answer 2

Here's the original from Blaise's work (he's actually not the author of the triangle, but whatever):

http://upload.wikimedia.org/wikipedia/commons/6/66/TrianguloPascal.jpg

Go to the 7th diagonal and over to the 3rd number.