I've been reviewing permutations, and I'm curious to see if I've mastered some of the basics. How would you evaluate the following?
Let's say you have (and I'm making this example up from scratch):
-- A seven-character license plate
-- The first four characters must each comprise a letter, and no letter can be repeated
-- The last three characters must each comprise a digit, and no number can be repeated
Using the multiplication axiom, would the answer therefore be:
[spoiler]26 * 25 * 24 * 23 * 10 * 9 * 8[/spoiler] ... whatever heinous number that turns out to be? ... which can also, I assume, be expressed as 26P4 times 10P3?
If that's correct ... how would the answer change if we kept all of the same conditions as the above example, but now we decided that the order of the characters doesn't matter, so long as we end up with 4 letters and 3 digits? (And you still can't repeat a character.)
Using the multiplication axiom, would the answer then be:
[spoiler]
36 * 35 * 34 * 33 * 32 * 31 * 30
[/spoiler] ... also expressed as 36P7?
Let's say you have (and I'm making this example up from scratch):
-- A seven-character license plate
-- The first four characters must each comprise a letter, and no letter can be repeated
-- The last three characters must each comprise a digit, and no number can be repeated
Using the multiplication axiom, would the answer therefore be:
[spoiler]26 * 25 * 24 * 23 * 10 * 9 * 8[/spoiler] ... whatever heinous number that turns out to be? ... which can also, I assume, be expressed as 26P4 times 10P3?
If that's correct ... how would the answer change if we kept all of the same conditions as the above example, but now we decided that the order of the characters doesn't matter, so long as we end up with 4 letters and 3 digits? (And you still can't repeat a character.)
Using the multiplication axiom, would the answer then be:
[spoiler]
36 * 35 * 34 * 33 * 32 * 31 * 30
[/spoiler] ... also expressed as 36P7?
