If no digit may be used more than once, how many 2-digit numbers can be formed using only the digits 5, 6, 3, and 2?
4 choices for each digit, so 4*4 values
The answers are:
11
12
10
2
My bad. I thought I read that digits could be repeated. So, the answer is 4*3 = 12
To find the number of 2-digit numbers that can be formed using the digits 5, 6, 3, and 2 without repeating any digit, we can use the concept of permutations.
In this case, we need to select 2 digits from a set of 4 digits (5, 6, 3, and 2), without repetition. The order of selection also matters, as it will result in different numbers.
The formula for finding permutations is given by:
P(n, r) = n! / (n - r)!
Where:
- n is the total number of items (digits in our case)
- r is the number of items to be selected (2-digit numbers in our case)
- ! denotes factorial, which means multiplying all positive integers from 1 up to that number
So, let's calculate the number of 2-digit numbers using the given formula:
P(4, 2) = 4! / (4 - 2)!
P(4, 2) = 4! / 2!
P(4, 2) = (4 x 3 x 2 x 1) / (2 x 1)
P(4, 2) = 24 / 2
P(4, 2) = 12
Thus, there are 12 different 2-digit numbers that can be formed using the digits 5, 6, 3, and 2 without repeating any digit.