A bag contains 5 red counters, 4 blue counters and k k\,k green counters, where k k\,k is a positive integer. Two counters are removed at random, without replacement.
The probability that both counters are green is 17\displaystyle \frac{1}{7}71.
Show that k2−4k−12=0k^2 - 4k - 12 = 0k2−4k−12=0.
Hence find the value of kkk.