Probability problem involving hyper-geometric distribution

n balls are chosen randomly and without replacement from an urn containing N white balls and M black balls. Give the probability mass function of the random variable X which counts the number of white balls chosen. Show that the expectation of X is $\frac{Nn}{(M+N)}$.

Hint: Do not use the hypergeometric distribution. Instead, write $X={X}_{1}+{X}_{2}+...+{X}_{N}$ where ${X}_{i}$ equals 1 if the ith white ball was chosen.

n balls are chosen randomly and without replacement from an urn containing N white balls and M black balls. Give the probability mass function of the random variable X which counts the number of white balls chosen. Show that the expectation of X is $\frac{Nn}{(M+N)}$.

Hint: Do not use the hypergeometric distribution. Instead, write $X={X}_{1}+{X}_{2}+...+{X}_{N}$ where ${X}_{i}$ equals 1 if the ith white ball was chosen.