JUST QUESTION 4

ms),- = 4. Let k be a positive integer, and let n1, 12,..., nk be non-negative integers. We have seen that the q-multinomial coefficient ni + 12+...+nk [ni + 12 + + nul! ni, 72, ..., [n 1]! [12], -- [nk]!! is a polynomial in q. Find as simple a formula as you can for the degree. Check that your formula is consistent with the known formulas for the degree of the q-factorial [k](by taking ni = n2 = ... = = nk = 1), the q-binomial coefficient (10 points) []!, 0