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let Xi be the random variable representing the ith role of a six-sided die and let xi be the rolled (observed) value of the ith roll

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let Xi be the random variable representing the ith role of a six-sided die and let xi be the rolled (observed) value of the ith roll. Assume that we roll the die N times and that each Xi is an i.i.d. sample.
(A) Because each Xi is i.i.d., we can work with a single distribution p(X = k). Define ck as the number of times that we observed a k among our N rolls: ck = X N i=1 (1 if Xi = k otherwise 0). (1)
We define p(X = k) = ck Z , where Z is a constant that ensures p sums to one: X k p(X = k) = X k ck Z = 1. (2)
Compute (write mathematical expression for) Z.