The required value is 70. Using the permutations formula the required value is calculated. I.e., P(76, x) = P(76, 70).
How to calculate permutations?
The formula for permutations is
nPr = P(n, r) = n!/(n - r)!
Where P -number of permutations,
n - number of objects in the given set
r - number of choosing objects
Calculation:
The given series is
76 × 75 × 74 × ... × 6 = P(76, x)
We know that,
76! = 76 × 75 × 74 × ... × 1 ...(i)
But to get the required series,
Divide the equation (i) by 6! = (76 - 70)!
Then,
76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6
So, x = 70.
That is,
n!/(n - r)! = P(n, r)
⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108
Hence the required x value is 70.
Learn more about the permutations here:
https://brainly.com/question/1216161
#SPJ1
