You are creating two different random numbers. You set the picker with one and choose a word from the word list with the other. Instead, create one random number. Use it for both operations:
- (IBAction)spin:(id)sender {
NSUInteger number = arc4random_uniform(words.count);
[pickerView selectRow:number inComponent:0 animated:YES];
selectedItem = words[number];
label.text = selectedItem;
}
This assumes the words in the picker match the words in the words
array.