Bob is playing a coin flipping game with 9 of his friends. They are each trying to predict the exact order of the outcomes of 20 flips (heads or tails). A person gets one point for predicting the outcome of a given flip (ie predicting the 3rd flip will be a heads would be one point if it turns out to be true, or predicting the 10th flip will be tails would be a point if it turns out to be true). The person who gets the most points wins. The coin is equally weighted.

Given the predictions of his friends and himself, what is a formula that gives the number of ways Bob can win?

Do you need all of their predictions to solve this question? Why or why not?