10 LED's that are supposed to be red but aren't!

The second illustration from the page you found is how to do it. They have used a 1000mF, I think that 1000nF would be enough and mF may be an error.

The delay was meant as a slow down of the update frequency for the LED's. This is how it should have been:

#include <Adafruit_NeoPixel.h>

#define PIN 6
#define PIX 10

Adafruit_NeoPixel strip = Adafruit_NeoPixel(PIX, PIN, NEO_GRB + NEO_KHZ800);

void setup() {
  // put your setup code here, to run once:

  strip.begin();
  strip.show();

}

void loop() {
  // put your main code here, to run repeatedly:

  for(int i = 0; i<strip.numPixels(); i++)
  {
    //Animate the strip here
    strip.setPixelColor(i,255,0,0);
  }

  //Only call this when brightness actually changes
  strip.setBrightness(5);

  //Only call this once per update / loop. It will send all changes
  //to the strip, thus updating all LED's
  strip.show();

  //Wait a bit before next update of the strip. You should avoid the
  //usage of delay if possible. Use timing with millis() instead.
  delay(100);

}