ROBERT THE THIEF
Robert is a thief, he is trying to steal the crown jewels. One problem, to access the jewels he needs to unlock a code with the numbers...
1, 0, 8, 6, 7, 5, 4, 3, 1, 0, 6, 2,
a) How many possibilities are there?
WHY? You set it up like this so you can see the different amount of numbers you need. Then the first space you put 12 because you have 12 different numbers to choose from. Then the next space you only have 11 because you just used one in the place before it. You then multiply all the numbers together to get the answer.
b) If the first two numbers cannot be a 0 or 6 how many possibilities are there?
WHY? The first number cannot be 6 or 0 so since there are four of those two numbers you can only have eight options, for the second space one number of the numbers you can choose from is gone so now you only have seven options. For the third space you can now include the 6 and 0's but you've already used two of the twelve spaces so now you only have ten options and so on.
c) If the first has to be a 0 and the fifth has to be 2 and the last 8 how many possibilities are there?
WHY? Te first place has only one option and same as the fifth and last place. The rest you just fill in with however many options you have like we did on the ones above.
1, 0, 8, 6, 7, 5, 4, 3, 1, 0, 6, 2,
a) How many possibilities are there?
WHY? You set it up like this so you can see the different amount of numbers you need. Then the first space you put 12 because you have 12 different numbers to choose from. Then the next space you only have 11 because you just used one in the place before it. You then multiply all the numbers together to get the answer.
b) If the first two numbers cannot be a 0 or 6 how many possibilities are there?
WHY? The first number cannot be 6 or 0 so since there are four of those two numbers you can only have eight options, for the second space one number of the numbers you can choose from is gone so now you only have seven options. For the third space you can now include the 6 and 0's but you've already used two of the twelve spaces so now you only have ten options and so on.
c) If the first has to be a 0 and the fifth has to be 2 and the last 8 how many possibilities are there?
WHY? Te first place has only one option and same as the fifth and last place. The rest you just fill in with however many options you have like we did on the ones above.
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