Theory question 104
Permutations and CombinationsIf 5yC2 = 190, find the value of y.
Show the model answer
Model answer
5y(5y − 1)/2 = 190, so 25y² − 5y − 380 = 0, i.e. 5y² − y − 76 = 0.
(5y + 19)(y − 4) = 0.
y must make 5y a positive integer, so y = 4.
Explanation
ⁿC₂ = n(n − 1)/2.