14, 32, and 50
None, because you do not have three even digits. None, because you do not have three even digits. None, because you do not have three even digits. None, because you do not have three even digits.
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.
To solve this question, two cases must be considered:Case 1: The three-digit even number ends with 0.If the three-digit number ends with 0, then the number must be even. After the digit 0 is used, six digits remain. After any one of these six digits is chosen to be the first digit, five digits remain. To complete the number, any of the five remaining digits could be chosen to be the second digit of the number.___6___ * ___5___ * ___1___ = 30 three-digit even numbers ending in 0.1st digit-------2nd digit----3rddigit (0)Case 2: The three-digit even number does not end with 0.If the three-digit number does not end with 0, it can end with 2 or 4. Therefore, there are two possibilities for the third digit. The first digit could be any of the remaining digits, EXCEPT 0: if 0 were the first digit, it would not be a three-digit number. Therefore, there would be five possible digits for the first digit. 0 could be used as the second digit, along with the four remaining digits that were not previously used.___5___ * ___5___ * ___2___ = 50 three-digit even numbers not ending in 0.1st digit-------2nd digit-----3rddigit (0)The total number of three-digit even numbers is 80, since 30 three-digit even numbers ending in 0 plus 50 three-digit even numbers not ending in 0 equals 80.
1348.
To find the even two-digit numbers where the sum of the digits is 5, we need to consider the possible combinations of digits. The digits that sum up to 5 are (1,4) and (2,3). For the numbers to be even, the units digit must be 4, so the possible numbers are 14 and 34. Therefore, there are 2 even two-digit numbers where the sum of the digits is 5.
To form a three-digit even number with different digits using the digits 0, 1, and 2, the last digit must be even, which can only be 0 or 2. If the last digit is 0, the first digit can be either 1 or 2 (2 options), and the middle digit will take the remaining digit (1 option). This gives us 2 valid numbers: 120 and 210. If the last digit is 2, the first digit can only be 1 (since it cannot be 0), and the middle digit must be 0. This gives us 1 valid number: 102. In total, there are 3 different three-digit even numbers: 120, 210, and 102.
There are 5760 such numbers.
5 x 10 x 5 = 250 different numbers, assuming there is no limit to each digits' use.
The final digit must be a 2 to form an even number. The first digit may be any of three remaining digits (1, 3, 5) while the second digit may be any of the two remaining digits. All together, that makes 3*2 = 6 distinct even numbers.
To find the three-digit numbers where the middle digit is the arithmetic mean of the other two digits, we denote a three-digit number as ( abc ), where ( a, b, c ) are its digits. The condition means ( b = \frac{a + c}{2} ), which implies ( a + c ) must be even. For ( a ) (1-9) and ( c ) (0-9), ( b ) must be an integer and a digit (0-9). The pairs ( (a, c) ) that yield valid integers for ( b ) can be counted, leading to 45 valid combinations for three-digit numbers. Thus, there are 45 such three-digit numbers where the middle digit is the arithmetic mean of the other two.
1000there aren't even 1000 three-digitnumbers...There are the digits 1 through 9 for the first digit. Then, we have 0 through 9 for the second digit - excluding the first digit. For the third digit, we have 0 through 9, excluding the two previous digits for a total of 9*9*8 =81*8 =648 three digit numbers with distinct digits.EDIT- ... to be a little more specific, if your talking about a 3-digit password or unlock code its would be 1000. _-_
There are 41 of them.