The symbol ₁₂P₉ represents the permutations of 9 quantities out of 12.
By definition,
From the calculator,
12! = 479,001,600
3! = 6
Therefore
₁₂P₉ = 479001600/6 = 79,833,600
Answer: 79,833,600
The correct solution is 75.
The problem presented with the word used as "divied" is very tricky and misleading to the point that it might create an understanding.
So we will approach this is in two ways.
If this was meant to be "divided by" then it would look like this:
6 / 192
If this was meant to be "divided to" then it would look like this:
192 / 6
Let us first solve for the first possible problem:
6 / 192 = ?
0.0312
0.0312 would be the answer.
Let us then solve for the second possible problem:
192 / 6 = ?
32 = ?
32 would be the answer.
So 0.0312 and 32 would be two possible answers to this problem.
Answer:
The even numbers between 0 and X represents an arithmetic sequence with a common difference of 2
The rule of arithmetic sequence = a + d(n - 1)
Where a is the first term and n is the number of terms
So, for the even numbers between 0 and X
The first term = a = 0
d = 2
So, we need to find n at the last term which is X
∴ X = 0 + 2 ( n -1 )
∴ n - 1 = X/2
∴ n = X/2 + 1
The sum of the arithmetic sequence = (n/2) × (2a + (n−1)d)
Substitute with a and d and X
So, the sum = (n/2) * (2*0 + (n−1)*2)
= (n/2) * ((n−1)*2)
= n(n-1)
= (X/2 + 1) * (X/2)
= X/2 by (X/2 + 1)
So, The quick way to add all even numbers between 0 and X always works.
