if the repetition is not allowed then the arrangement can be 3*2*1 = 6 ways
if repetition is allowed the ways can be 6*6*6= 216 ways
if repeating is allowed... 36 (6x6, for the last two digits) If not, 6 (3x2, last two digits)
3!=6
If repeated digits are allowed, then the largest 12-digit number is 999,999,999,999 .If repeated digits are not allowed, then the largest 12-digit number is 989,898,989,898 .If the same digit can't be used more than once, then the largest possible number has only10 digits. The number is 9,876,543,210 .
There are 2 possible digits for the first digit (3 or 4), leaving 3 possible digits for the second digit (5 and 6 and whichever was not chosen for the first), leaving 2 possible digits for the third. Thus there are 2 × 3 × 2 = 12 possible 3 digit numbers.
Assuming the the last part of the question is that the sequence may not END in 000, there are 2997 sequences.
There are 30,240 different 5-digit numbers. Math: 10*9*8*7*6 1st digit has 10 possible choices (0-9) 2nd digit has 9 possible choices (one of the digits was used in the 1st digit) 3rd digit has 8 possible choices 4th digit has 7 possible choices 5th digit has 6 possible choices
There are two possible digits for the first and last digit, and two possible digits for the centre digit, making 2 × 2 = 4 possible 3 digit palindromes from the set {1, 2}, namely the set {111, 121, 212, 222}.
10 digits to select for the first number in the sequence 10 digits to select for the second number in the sequence for each possible option of 10 digits in the first slot in the sequence (10 * 10) 10 digits to select for the third number in the sequence for each possible option of 10 digits in the second slot for each possible digit in the first slot of the sequence (or more easily put, 10 possible digits for each of 100 potential first two number sequences) [10*10*10] etc.... =10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^7 = 10,000,000 (10 Million) Now add an area code before that 7 digit phone number and you get 10 Billion combinations (of course there are exclusions such as any sequence starting in 911 would be prohibited which is a reduction of 10 million numbers itself - 911 000 0001, 911 000 0002, etc. There are many other exclusions as well such as can't start with 0 - this removes another 1 billion sequences)
There are seven possible digits for the first digit and 6 digits for the second (minus one digit for the digit used as the first digit) and 5 options for the last digit (minus one again for the second digit) and then you just multiply them all together to get a total possible combination of 210 numbers that are possible.
what is the greets possible 9 digit number that uses each of the digits 1-3 times
If repetition of digits isn't allowed, then no13-digit sequencescan be formed from only 5 digits.
Assuming that 2356 is a different number to 2365, then: 1st digit can be one of four digits (2356) For each of these 4 first digits, there are 3 of those digits, plus the zero, meaning 4 possible digits for the 2nd digit For each of those first two digits, there is a choice of 3 digits for the 3rd digit For each of those first 3 digits, there is a choice of 2 digits for the 4tj digit. Thus there are 4 x 4 x 3 x 2 = 96 different possible 4 digit numbers that do not stat with 0 FM the digits 02356.