Find the number of distinct/ dissimilar terms in the expansion of $(x + y + z + w)^{n}$

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Solution

$n u m b e r o f t e r m s i n t h e e x p a n s i o n o f (x_{1} + x_{2} + . . . . . . . + x_{r})^{n} i s^{n + r - 1} C_{r - 1} ∴ n u m b e r o f d i s t i n c t t e r m s =^{n + 4 - 1} C_{4 - 1} = n + 3 C_{3} = (\frac{(n + 3)!}{n! \times 3!}) = (\frac{(n + 3) (n + 2) (n + 1)}{6})$

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