This problem involves drawing three cards from a deck of cards. Assume that the deck contains 3 aces, 5 other face cards, and 11 non-face cards, and that you randomly draw 3 cards. A random variable Z is defined to be 5 times the number of aces plus 4 times the number of other face cards drawn. How many different values are possible for the random variable Z?

Answer with Step-by-step explanation:We are given that Number of ace cards=3Number of face cards=5Number of non-face cards=11When we draw randomly 3 cards.Z=5(number of aces)+4(number of other face cards)We have to determine the possible different values for the random variable ZNumber of ace cards=3, number of other face cards=0Z=5(3)+4(0)=15Number of ace cards=2, number of other face cards=1[tex]z=5(2)+4(1)=14[/tex]Number of ace card=1, number of other face  cards=2Z=5(1)+4(2)=13Number of ace card=0, number of other face cards=3Z=5(0)+4(3)=12