How many 5 digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6 if repeition are not allowed.
do i use 7P5? since i am choosing 5 numbers from 7 and they can't be repeated?
You have 6 choices for the first digit, which cannot be zero, six for the second digit (which can be zero), five for the third digit, then four and then 3.
That makes 6*6*5*4*3 = 2160 possibilities
To find the number of 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition, you can use the concept of permutations.
The formula for permutations is given by nPr, where n is the total number of items to choose from and r is the number of items to select.
In this case, you have 7 digits to choose from (0, 1, 2, 3, 4, 5, 6) and you need to select 5 digits to form a 5-digit number.
So, you can calculate the number of possible combinations using the formula 7P5 (7 permutations 5):
7P5 = 7! / (7 - 5)!
= 7! / 2!
= (7 x 6 x 5 x 4 x 3) / (2 x 1)
= 5040 / 2
= 2520
Therefore, there are 2520 different 5-digit numbers that can be formed using the digits 0, 1, 2, 3, 4, 5, and 6 without repetition.