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The number of terms in the expansion of the multinomial ${(x + y + z)}^{n}$

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12(n+1)(n+2)

12n(n+1)

12(n+1)(n+3)

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detailed solution

Correct option is A

Number of terms in (x+y+z)n= number of non-negative integral solution of p+q+r=n=n+2C2=12(n+2)(n+1)

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The number of terms in the expansion of the multinomial (x + y + z)n

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The number of terms in the expansion of the multinomial ${(x + y + z)}^{n}$