Question 1 Report
\(^{5y}{C}_2\) = 190, find the value of y
We can use the formula for combinations to solve for y:
5yC2 = (5y)! / (2!(5y-2)!) = 190
Expanding the factorials:
(5y)(5y-1) / 2 = 190
Solving for y:
(5y)(5y-1) = 380
25y^2 - 5y = 380
25y^2 - 5y - 380 = 0
Using the quadratic formula:
y = (-b ± √(b^2 - 4ac))/(2a)
y = (-(−5) ± √((-5)^2 - 4(25)(-380)))/(2(25))
y = (5 ± √(25 + 90000))/(50)
y = (5 ± √(90025))/(50)
Taking the positive root:
y = (5 + 300)/(50)
y = 305/50
y = 6.1
So the value of y is approximately 6.1.
Answer Details
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