How many total distinct terms are there in the expansion of $(x + y + z + t)^{10}$

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Solution

Applying the formula $^{n + r - 1} C_{r - 1}$ where $n = 10; r = 4$ we get $^{10 + 4 - 1} C_{4 - 1} =^{13} C_{3} = \frac{13 \times 12 \times 11}{3!} = 2 \times (143) = 286$ .

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