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There are 10,000 possible 4-digit combinations for a phone that dials 0 through 9 if repetition is allowed. Some of the combinations include {0,0,0,0}, {9,9,9,9} and all arrangements between. Since the order of digits matters ({0,0,0,1} is not equal to {0,0,1,0}) and repetition is allowed (each digit can be in any of the four positions), the arrangements are called "permutations with repetition."
Know MoreAccording to Math Is Fun, permutations with repetition are the easiest to calculate. The person needs to determine the number of dial pad numbers she can choose from (n) and the number of selections (r). In this case, to calculate a 4-digit number with numbers 0 through 9 available, there are 10 available dial pad numbers (n=10) for each digit with four digits selected (r=4). The number of permutations can be calculated with the formula n^r, in this case by multiplying 10 x 10 x 10 x 10.
When repetition is not allowed, the permutation formula is adjusted to the factorial function, which is noted by ?!? and is simply a multiplication of a series of descending natural numbers. The formula is useful in the cases when each number can be selected only once. For example, if there are 10 competitors in the race (n=10), and the first four get a reward (r=4), a person can calculate the number of possible reward distribution combinations by dividing n!, which is 10x9x8x7x6x5x4x3x2x1, with the factorial function of the difference between n and r (n-r)!.
When the order does not matter, such as in lottery drawings, the calculations are called combinations.
Learn MoreThere are a total of 10,000 four-digit combinations using the numbers 0 to 9, assuming that 0 is allowed as the first digit and repetition of digits is allowed. Some of the possible combinations are 1911, 0000, 3145 and 2458.
Full Answer >There are 90,000 different number combinations that can be made in a five-digit number if numbers can repeat. To determine the number of possibilities, each place digit has to be evaluated independently to see how many numbers could fit there and then all are multiplied together.
Full Answer >There are 720 different combinations for a seven-digit number. This answer can be found using the (n[n-1][[n-2] ... to k factors)/k!, where n is the possible number of digits and k is the number of digits in the number. For a seven-digit number, the formula is 10!/7!.
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