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TS EAMCET · Maths · Permutation Combination

The number of non negative integral solutions of the equation \(x+y+z+t=10\) when \(x \geq 2, z \geq 5\) is

  1. A \(80\)
  2. B \(20\)
  3. C \(50\)
  4. D \(10\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(20\)

Step-by-step Solution

Detailed explanation

Let \(x = x' + 2, z = z' + 5\), where \(x', y, z', t \geq 0\). \((x' + 2) + y + (z' + 5) + t = 10\) \(x' + y + z' + t = 3\) Number of solutions = \(\binom{3+4-1}{4-1} = \binom{6}{3}\) \(\binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20\)