How many positive 4-digit integers contain the digit grouping 73 at least once? For instance, 2738 and 7344 are two such integers to include, but 2378 and 5703 do not meet the restrictions.
+50 cases: 73 is in the front, middle or end.
case where it is the front:
first - second digit, 1 choice each
3rd digit: 1~9 = 9
4th : 9
case where it is the middle:
first digit has 9 choices, and the 4th also has 9 choices. 2nd and 3rd have one choice.
case where it is the end.
same thing, first digit 9 choices, 2nd digit 9 choices, 3 and 4, 1 choice.
So! 9 times 9+9 times 9+9 times 9 = ill leave that to you
+37159 73 xx x can be 0-9 100 choices
x73y x can be 1- 9 y can be 0 - 9 90 choices
xy 73 x can be 1-9 y can be 0-9 90 choices
total choices = 280
+313 cases: 73 is in the front, middle or end.
case where it is the front:
first - second digit, 1 choice each
3rd digit: 1~9 = 9
4th : 9
case where it is the middle:
first digit has 9 choices, and the 4th also has 9 choices. 2nd and 3rd have one choice.
case where it is the end.
same thing, first digit 9 choices, 2nd digit 9 choices, 3 and 4, 1 choice.
So! (9 times 9)+(9 times 9)+(9 times 9) = ill leave that to you
