Question
Question: If x<sub>i</sub>≥ i, the no. of integral solutions of the equation x<sub>1</sub> + x<sub>2</sub> + x...
If xi≥ i, the no. of integral solutions of the equation x1 + x2 + x3 + x4 = 40.
A
33C4
B
33C3
C
32C3
D
32C4
Answer
33C3
Explanation
Solution
x1 ≥ 1, x2≥ 2, x3 ≥ 3, x4 ≥ 4.
a = x1 0 1 ≥ 0, b = x2 - 2 ≥0, c = x3 - 3 ≥ 0, d = x4 - 4 ≥ 0.
a + b + c + d = 30.
∴ No. of solutions = 30+4−1C4−1=33C3.