The number of ways to Position r things in a certain order
where weh have n things and are positioning r of them
"n Position r" = "nPr" = n(n-1)(n-2)...(n-r+1) <- that is, until there
are exactly r factors.
Note that nP0 = 1 because there is 1 way to position 0 or none of them.
That 1 way is to simply to not position any of them! :)
how many 'words' can be formed using the letter of "student" using each letter
at most once:
1. if each letter must be used
"student" has 7 letters, all different.
That "7 Position 7" or 7P7 = 7*6*5*4*3*2*1 = 5050 ways.
Here's why that formula works:
Choose the 1st letter any of the 7 ways.
Choose the 2nd letter any of the remaining 6 ways.
Choose the 3rd letter any of the remaining 5 ways.
Choose the 4th letter any of the remaining 4 ways.
Choose the 5th letter any of the remaining 3 ways.
Choose the 6th letter either of the remaining 2 ways.
Choose the 7th letter only the remaining 1 way.
That's 7*6*5*4*3*2*1 = 7! = 7P7 = 5040
2. if some or all the letter may be omitted
That's 7P0+7P1+7P2+7P3+7P4+7P5+7P6+7P7
or
1+7+42+210+840+2520+5040+5040 = 13699
Edwin
