If repetition is allowed and order is important, then you have essentially a base-4 number system, with the numbers ranging from 00004 to 33334. The quantity of permutations in this example is 44 = 256. If repetition is not allowed, but order is important, then it is 4! = 24.
* * * * *
The above answer is perfectly correct. But, as stated in the answer, for permutations. However, according to the mathematical definition of combinations (as opposed to permutations), the order is irrelevant to combinations. 1234 is the same as 1423 or 4213 etc. Consequently, there can be only one 4-number combination from 4 numbers
45
To calculate the number of license plate combinations using three letters and four numbers, we consider the possibilities for each part separately. There are 26 letters in the English alphabet, so for three letters, there are (26^3) combinations. For the four numbers, using digits 0-9, there are (10^4) combinations. Therefore, the total number of combinations is (26^3 \times 10^4), which equals 17,576,000 combinations.
The number of combinations of six numbers that can be made from seven numbers will depend on if you can repeat numbers. In all there are over 2,000 different numbers that can be made.
10
How many four digit combinations can be made from the number nine? Example, 1+1+2+5=9.
2 to the 7th power = 128 * * * * * No. That is the total number of combinations, consisting of any number of elements. The number of 2 number combinations is 7*6/2 = 21
8C6 = 28
9!/5! or 3024
None. You do not have enough numbers to make even one combination.
Like 1235 or 8067? If you allow leading zeros, then 10 000. If you disallow leading zeros, then 9 000. * * * * * Those are the numbers of PERMUTATIONS, not COMBINATIONS. In combinations the order does not matter, so 1234 = 4312 = 2314 etc. The number of combinations is (10*9*8*7)/(4*3*2*1) = 210. The question of leading 0s does not arise because there is no order to the set of numbers in the combination so there is no "leading".
Using the formula n!/r!(n-r)! where n is the number of possible numbers and r is the number of numbers chosen, there are 13983816 combinations of six numbers between 1 and 49 inclusive.
20