To solve simple equations like this, it's essential to apply the order of operations defined by PEMDAS. This acronym represents the sequential operations needed for solving equations. PEMDAS indicates Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. According to PEMDAS, multiplication takes precedence over addition, leading us to: 5 + [1*10] = 5 + 10 = 15.
3003. We seek to determine the number of ways to select 10 players from a group of 15 players, with the goalie being fixed. The number of unique combinations can be calculated using the combination formula. The total comes to 3003 distinct lineups.