Hello, saberteeth!

We have to "talk" our way through these . . .

There are two cases to be considered:1) A number of 4differentdigits is formed using the digits {1,2,3,4,5,6,7}.

How many numbers can be formed that are greater than 3400?

. . [1] The first digit is 3.

. . [2] The first digit is 4 or more.

[1] The 1st digit is 3: .

. . .The 2nd digit must be {4,5,6,7} . . . 4 choices.

. . .The 3rd digit has 5 choices.

. . .The 4th digit has 4 choices.

There are: . numbers greater than 3400 which begin with 3

[2] The 1st digit is 4 or more.

. . .The 1st digit must be {4,5,6,7} . . . 4 choices.

. . .The 2nd digit has 6 choices.

. . .The 3rd digit has 5 choices.

. . .The 4th digit has 4 choices.

There are: . other numbers greater than 3400.

Therefore, there are: . numbers greater than 3400.

These are all 3-digit numbers.2) How many numbers ofdifferentdigits lying between 100 and 1000

can be formed with the digits {0,2,3,4,8,9}?

The first digit can be: {2,3,4,8,9} . . . 5 choices.

The second digit has 5 choices.

The third digit has 4 choices.

Therefore, there are: . such numbers.