i asked a question yesterday and i got an answer. my question was how many 7 digit numbers can be formed with the numbers 1,2,4,7 if
a) repetation is allowed
b) repetation is not allowed
i got an answer but i needed 2 answers and im not sure if the answer was for a or b
To determine the number of 7-digit numbers that can be formed with the numbers 1, 2, 4, and 7, with repetition allowed or not allowed, let's break down the two cases:
a) When repetition is allowed:
In this case, we can choose any of the four available numbers (1, 2, 4, or 7) for each of the seven positions in the number. Since repetition is allowed, we have four options for each position. Therefore, the total number of possibilities can be calculated by multiplying these options together:
Total number of possibilities = 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^7 = 16,384
So, if repetition is allowed, there are 16,384 different 7-digit numbers that can be formed using the numbers 1, 2, 4, and 7.
b) When repetition is not allowed:
In this case, once we choose a number for a particular position, we cannot choose the same number for any other position. For the first position, we have four options (1, 2, 4, or 7). After choosing a number for the first position, we have three remaining options for the second position (since one number is already chosen). Similarly, for each subsequent position, the number of available options decreases by one.
To calculate the total number of possibilities, we multiply the number of options for each position:
Total number of possibilities = 4 x 3 x 2 x 1 x 1 x 1 x 1 = 4! = 24
Therefore, if repetition is not allowed, there are 24 different 7-digit numbers that can be formed using the numbers 1, 2, 4, and 7.
Based on the given information, the answer provided earlier was likely for case (a) where repetition is allowed.