For the multinomial expansion ( 2 x − 3 y + z ) 10 = ∑ α + β + γ = 10 α ! β ! γ ! 10 ! ( 2 x ) α ( − 3 y ) β z γ , where α , β , γ are nonnegative integers, which statements are correct?

Question

For the multinomial expansion ( 2 x − 3 y + z ) 10 = ∑ α + β + γ = 10 ​ α ! β ! γ ! 10 ! ​ ( 2 x ) α ( − 3 y ) β z γ , where α , β , γ are nonnegative integers, which statements are correct?

TestHub · Accepted Answer

(A) The count is ( 2 12 ​ ) = 66 . (B) Put all three multinomial variables equal to 1. (C) The coefficient is 2 ! 3 ! 5 ! 10 ! ​ 2 2 ( − 3 ) 3 = − 9 ⋅ 10 ! /5 ! . (D) Put x = y = z = 1 in ( 2 x − 3 y + z ) 10 .

Mathematics - Binomial Theorem Question with Solution | TestHub

Options:(select one or more)

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