+0

# Permutations.....

0
267
5

How many permutations are there for all 10 numbers from 0 to 9 taken 3 at a time, if the 3 numbers cannot begin with a zero, that is: 012 not allowed but 102...etc, allowed? I thank you for help.

Mar 4, 2018

#1
+18138
+2

My guess

you cannot have   0  then 9 x 8   numbers = 72 numbers

out of   10 p 3 = 720      720 - 72 = 648 combos

Mar 4, 2018
#2
+2

EP is right. There are 10P3 = 720 permutations of the 10 numbers from 0 to 9. Since each permutation begins with one of 10 digits, including zero, then there should be:720 / 10 =72 permutations that will begin with zero. Therefore, the total number of permutations excluding zero at beginning would be: 720 - 72 = 648. Here is a list of ALL numbers that begin with zero. You may count them and should get 72:

{0, 1, 2} | {0, 1, 3} | {0, 1, 4} | {0, 1, 5} | {0, 1, 6} | {0, 1, 7} | {0, 1, 8} | {0, 1, 9} | {0, 2, 1} | {0, 2, 3} | {0, 2, 4} | {0, 2, 5} | {0, 2, 6} | {0, 2, 7} | {0, 2, 8} | {0, 2, 9} | {0, 3, 1} | {0, 3, 2} | {0, 3, 4} | {0, 3, 5} | {0, 3, 6} | {0, 3, 7} | {0, 3, 8} | {0, 3, 9} | {0, 4, 1} | {0, 4, 2} | {0, 4, 3} | {0, 4, 5} | {0, 4, 6} | {0, 4, 7} | {0, 4, 8} | {0, 4, 9} | {0, 5, 1} | {0, 5, 2} | {0, 5, 3} | {0, 5, 4} | {0, 5, 6} | {0, 5, 7} | {0, 5, 8} | {0, 5, 9} | {0, 6, 1} | {0, 6, 2} | {0, 6, 3} | {0, 6, 4} | {0, 6, 5} | {0, 6, 7} | {0, 6, 8} | {0, 6, 9} | {0, 7, 1} | {0, 7, 2} | {0, 7, 3} | {0, 7, 4} | {0, 7, 5} | {0, 7, 6} | {0, 7, 8} | {0, 7, 9} | {0, 8, 1} | {0, 8, 2} | {0, 8, 3} | {0, 8, 4} | {0, 8, 5} | {0, 8, 6} | {0, 8, 7} | {0, 8, 9} | {0, 9, 1} | {0, 9, 2} | {0, 9, 3} | {0, 9, 4} | {0, 9, 5} | {0, 9, 6} | {0, 9, 7} | {0, 9, 8} | {1, 0, 2} | {1, 0, 3} | {1, 0, 4} | {1, 0, 5} | {1, 0, 6} | {1, 0, 7} | {1, 0, 8} | {1, 0, 9} | ... (total: 720)

Mar 4, 2018
#3
+18138
0

Holy Guacamole !  I hope you didn't TYPE all of those !      I'd have at LEAST  10 C 3   typos !

ElectricPavlov  Mar 4, 2018
#4
0

No EP!!. The computer did!!.

Mar 4, 2018
#5
+99736
+1

We have 9   ways to fill the first position  (1-9), 9 ways to fill the second position (every number 0-9 except the first one we chose) and 8 ways to fill the third position (every number 0-9 except the first two we chose)  =  9 * 9 * 8    =  648

Mar 4, 2018