Question: Complete the details in the proof of the multinomial theorem. Multinomial theorem. For positive integers n, t, the coefficient of x1n1x2n2x3n3 . . . xtnt

Complete the details in the proof of the multinomial theorem.
Multinomial theorem.
For positive integers n, t, the coefficient of x1n1x2n2x3n3 . . . xtnt in the expansion of (x1 + x2 + x3 + . . . + xt)n is

where each ni is an integer with 0 ‰¤ ni ‰¤ n, for all 1 ‰¤ i ‰¤ t, and n1 + n2 + n3 + . . . + nt = n.

! ni!n2! n3! n,!

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