Hello,

#10: A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If Lizzie wants to write a report that includes two or three of the birds, how many different reports can she write?

Solution: First find the number of 2-bird reports - YYNNNN, then consider the number of 3-bird reports - YYYNNN, add them together.

HOWEVER, isn't it the case that if you pick one bird, you will have to pick another one? i.e. you wouldn't write 2 reports on the same bird?

Also:
#13: Mario's Pizza has 2 choices of crist: deep dish and thin-and crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions and pepperoni. Finally, Mario's offers every pizza in extra-cheese as well as regular. If Linda's volleyball team decides to order a pizza with four toppins, how many different choices do the teammates have at Mario's Pizza?

Solution: Consider the toppings first: YYYYN

HOWEVER, if they picked one topping, wouldn't they not pick it again?

Finally:
#7: A British spy is trying to escape from his prison cell. The lock requires him to enter one number, from 1-9, and then push a pair of colored button simultaneously. He can make one attempt every 3 seconds. If there are 6 colored buttons, what is the longest possible time it could take the spy to escape from the prison cell?

Solution: The different pairs of colored buttons - YYNNNN

HOWEVER, if he had to press the colored buttons simultaneously, then if he pressed one color button, couldn't he not press it again?

Thank you.

Yes to all three. The anagram grid method already factors this in. For example, the grid YYNNNN already says that you pick 2 (different) birds and do not pick the other four birds. The six letters represent the 6 different birds. And so on for the other examples.