The number of distinct terms in the expansion of $ (x+2 y-3 z+5 w-7 u)^{n} $ is

Question

The number of distinct terms in the expansion of $ (x+2 y-3 z+5 w-7 u)^{n} $ is, $ n+1 $, $ { }^{n+4} C_{4} $, $ { }^{n+4} C_{n+2} $, $ { }^{n} C_{4} $

MARKS App · Accepted Answer

We know that the number of distinct terms in the multinomial expansion of x 1 + x 2 + … + x n m is given by C n - 1 n + m - 1 . Therefore, number of distinct terms in the expansion of ( x + 2 y - 3 z + 5 w - 7 u ) n is = C 5 - 1 n + 5 - 1 = C 4 n + 4

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