How many numbers can be formed by multiplying some or all of the numbers 2,3,4,5,6,7,8?
The answer is 48 but I don't know how to get there?
To find the number of possible numbers that can be formed by multiplying some or all of the numbers 2, 3, 4, 5, 6, 7, and 8, we can use the concept of combinations.
Step 1: Calculate the total number of combinations.
To find the total number of combinations, we need to consider all possible subsets of the given numbers. Since each number can be either included or excluded, there are 2 possibilities for each number. Hence, the total number of combinations is obtained by multiplying the number of possibilities for each number.
In this case, we have 7 numbers (2, 3, 4, 5, 6, 7, 8), so the total number of combinations is 2^7 = 128.
Step 2: Exclude the empty set.
Since the empty set does not represent a valid number, we need to subtract it from the total number of combinations found in step 1.
Subtracting 1 (the empty set) from 128 gives us 128 - 1 = 127.
Step 3: Calculate the number of single-digit numbers.
We need to exclude the numbers that involve multiplication with multiple digits. Therefore, we need to identify the numbers that can be formed by multiplying only one of the given numbers.
In this case, each of the given numbers (2, 3, 4, 5, 6, 7, 8) can be multiplied individually, resulting in 7 single-digit numbers: {2, 3, 4, 5, 6, 7, 8}.
Subtracting 7 from the total number found in step 2 gives us 127 - 7 = 120.
Therefore, there are 120 numbers formed by multiplying some or all of the numbers 2, 3, 4, 5, 6, 7, and 8.