Question

The number of positive integral solutions of the equation \( x_1 + x_2 + x_3 + x_4 = 1050 \) is

• A. 1870
• B. 1875
• C. 1865
• D. 1880

Hint:

Use the stars and bars method to find the number of positive integer solutions to equations.

Answer 1

The Correct Option is B

Step 1: Applying the stars and bars method.
This is a typical application of the stars and bars method, which is used to find the number of solutions to an equation of the form \( x_1 + x_2 + \dots + x_n = N \), where each \( x_i \) is a positive integer. The solution is \( \binom{1050 - 1}{4 - 1} = 1875 \).

Step 2: Conclusion.
Thus, the correct answer is option (B).

Final Answer: \[ \boxed{\text{(B) } 1875} \]