Since the number must be even, the third digit must be either the 2 or the 6 = 2 choices.
For each of those . . .
The second digit can be any one of the 4 remaining ones. For each of those . . .
The first digit can be any one of the 3 remaining ones.
Total number of ways to line them up = 2 x 4 x 3 = 24
24 different numbers.
There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.
18
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
To form 2-digit numbers from the digits 5, 6, 3, and 2, we can use each digit as both the tens and units place. The possible combinations for the tens place are 5, 6, 3, and 2, giving us 4 options. For each choice of the tens digit, we have 4 choices for the units digit as well. Therefore, the total number of 2-digit numbers that can be formed is (4 \times 4 = 16).
5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.
24 different numbers.
There are 5 numbers of 1 digit, 25 numbers of 2 digits, and 75 numbers of 3 digits. This makes 105 numbers in all.
There are 3 values (1, 2, 3) for each of the 4 digits. Therefore, there are 3*3*3*3 or 81 four digit numbers that can be formed.
18
There are 9 digits that can be the first digit (1-9); for each of these there is 1 digit that can be the second digit (6); for each of these there are 10 digits that can be the third digit (0-9); for each of these there are 10 digits that can be the fourth digit (0-9). → number of numbers is 9 × 1 × 10 × 10 = 900 such numbers.
20
If the digits may not be repeated, there are 6x5x4x3x2x1 = 720 numbers, If digits can be repeated, the answer is 6x6x6x6x6x6 = 46,656 numbers If zero is ong the available digits but is excluded from the first place. 5x6x6x6x6x6=38,880 numbers
5 x 10 x 5 = 250 different numbers, assuming there is no limit to each digits' use.
9630
To form three-digit even numbers from the set {2, 3, 5, 6, 7}, we can use the digits 2 or 6 as the last digit (to ensure the number is even). For each case, we can choose the first two digits from the remaining four digits. For three-digit numbers, there are 2 options for the last digit and (4 \times 3 = 12) combinations for the first two digits, resulting in (2 \times 12 = 24) even numbers. For four-digit even numbers, we again have 2 options for the last digit. The first three digits can be selected from the remaining four digits, giving us (4 \times 3 \times 2 = 24) combinations for each last digit. Thus, there are (2 \times 24 = 48) even four-digit numbers. In total, there are (24 + 48 = 72) three-digit and four-digit even numbers that can be formed from the set.
If they can be repeated, 343 different numbers. If they can be used once each, there are only 210.