InterviewSolution
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InterviewSolution
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Find the number of non-negative integral solutions of equation `x+y+z+2w=20.` |
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Answer» If w=0, equation reduces to x+y+z=20. Number of non-negative inteegral solutions `= .^(20+3-1)C_(3-1) = .^(22)C_(2)` If w=1, equation reduces to x+y+z=18. Number of non-negative integral solutions `=(18+3-1)C_(3-1)= .^(20)C_(2)` Similarly, we get number of non-negative integral solutions for w=2, 3, .., 10. Hence, total number of solutions `=(22)C_(2)+ .^(20)C_(2)+ .^(18)C_(2)+..+ .^(2)C_(2)` |
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