How many integral solutions of X + X2 + X3+ X4 = 30 Satisfy X2, X7/0,...

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How many integral solutions of X₁ + X2 + X3+ X4 = 30 Satisfy X₁2, X₂7/0, X371-5 and xy > 8 ? There are 100 students at a school and three dormitories, A, B and C with capacities 25, 35 and 40 respectively. How many ways are there to fill the dormitories ? Determine the number of 11-permutations of the multiset S= 23.a, 4.b, 5.c}. How many integral solutions of X₁ + X2 + X3+ X4 = 30 Satisfy X₁2, X₂7/0, X371-5 and xy > 8 ? There are 100 students at a school and three dormitories, A, B and C with capacities 25, 35 and 40 respectively. How many ways are there to fill the dormitories ? Determine the number of 11-permutations of the multiset S= 23.a, 4.b, 5.c}.