In how many ways can you select a set of 3 letters from JasmineOrtz
if the order of selection matters?
There are no repeated letters, so all letters are distinguishable.
You can choose the first letter any of 11 ways.
That leaves 10 ways to choose the 2nd letter.
That leaves 9 ways to choose the 3rd letter.
That's 11∙10∙9 = 990 ways to choose 3 letters where order matters
In how many ways can you select a set of 3 letters if the order of selection does not matter?
For example, amt, atm, tam, tma, mat, mta are all counted among the 990 above,
but all of them are the same if the order they are in doesn't matter. So we
need to divide the 990 by the number of ways each one can be arranged, which
will remove the "extras" from the 990.
In the example amt, atm, tam, tma, mat, mta,
there are 3 ways to choose the 1st letter.
That leaves 2 ways to choose the 2nd letter.
That leaves 1 ways to choose the 3rd letter.
That's 3∙2∙1 = 6 ways. So each selection is counted 6 times too many among the
990, so we need to divide the 990 by 3∙2∙1 or 6:
It's the same for any group of 3 letters, so the answer is:
11∙10∙9 990
------- = --- = 165.
3∙2∙1 6
Edwin
