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Math 1313Section 5.31Section 5.3Generalized Multiplication PrincipleSuppose a task T1can be performed in N1ways, a task T2can be performed in N2ways,…, and , finallya task Tncan be performed in Nnways. Then the number of ways of performing the tasks T1, T2, …, Tnin succession is given by the productN1• N2•… •NnExample 1:A coin is tossed 3 times, and the sequence of heads and tails is recorded.a. Determine the number of outcomes of this activity.b. List the outcomes of this experiment by first drawing a tree diagram.Example 2:The Burger Bar offers the following items on its menu:BurgerSidesBeveragesDessertsSingle MeatFriesTeaCheesecakeDouble MeatOnion RingsCoffeeBrownieFruit BowlSodaCookieCheddar PeppersIce Cream ConeIf a customer chooses 1 item from each category, how many meals can be made? List 1 meal possible.
Math 1313Section 5.32Example 3:An identification number for employees at a certain company contains six digits. Howmany ID numbers are possible if repetition is allowed?Example 4:A license plate consists of 2 letters followed by 4 digits. How many license plates arepossible if the 1st letter can't be O, the 1st digit can't be 0 and no repetitions are allowed?Example 5:In the original plan for area codes in 1945, the first digit could be any number from 2through 9, the second digit was either 0 or 1, and the third digit could be any number except 0. With thisplan, how many different area codes were possible?Popper 5: