(Solved): Let k 2, n1, . . . , nk N and N = n1 + + nk. Define the multinomial coefficient N n ...

Let k ≥ 2, n1, . . . , nk ∈ N and N = n1 + · · · + nk. Define the multinomial coefficient N n1, n2, . . . , nk ! := N! n1!n2! . . . nk! . Show that N n1, n2, . . . , nk ! = N n1 ! N − n1 n2 ! N − n1 − n2 n3 ! . . . N − n1 − · · · − nk−1 nk !