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

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To handle constraints of the form $ x_i \ge k $, simply subtract the sum of all lower bounds $ k $ from the total sum $ N $ on the RHS. The new sum becomes $ N' = N - \sum k $. Then apply the standard formula $ \binom{N'+r-1}{r-1} $.

Updated On: Mar 26, 2026

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The Correct Option is B

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

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The Correct Option is B

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