This problem involves drawing three cards from a deck of cards. Assume that the deck contains 4 aces, 4 other face cards, and 15 non-face cards, and that you randomly draw 3 cards. A random...

This problem involves drawing three cards from a deck of cards. Assume that the deck contains 4 aces, 4 other face cards, and 15 non-face cards, and that you randomly draw 3 cards. A random variable ZZ is defined to be 5 times the number of aces plus 4 times the number of other face cards drawn.

10 values are possible for the random variable Z.

Fill in the table below to complete the probability density function. Be certain to list the values of ZZ in ascending order.