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.

Guest Jul 3, 2021

#1**+1 **

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

HELPplzplzplz Jul 3, 2021

#2**+2 **

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

ElectricPavlov Jul 3, 2021

#4**+1 **

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

apsiganocj Jul 4, 2021