If 2 different members are to be selected at random from a group of 8

If 22 different members are to be selected at random from a group of 88 people and if pp is the probability that both members selected will be older than 35 years old,
is p>13p>13?

(1) More than half of the group members are older than 35 years old.
(2) The probability that both members selected will be 35 years old or younger is greater than 1/10

1] No. of people >35 can be 5, 6, 7, 8

\(\frac{5c2}{8c2}\) =\(\frac{5*4}{8*7}\) = \(\frac{5}{14}\) > \(\frac{1}{3}\) = yes
\(\frac{6c2}{8c2}\) =\(\frac{6*5}{8*7}\) = \(\frac{15}{24}\) > \(\frac{1}{3}\) = yes
\(\frac{7c2}{8c2}\) =\(\frac{7*6}{8*7}\) = \(\frac{3}{4}\) > \(\frac{1}{3}\) = yes
\(\frac{8c2}{8c2}\) =\(\frac{8*7}{8*7}\) = \(\frac{1}{1}\) > \(\frac{1}{3}\) = yes

Hence A is sufficient

2] let's say n (> 35) = 4 & n1( <35 ) = 4
\(\frac{4c2}{8c2}\) + \(\frac{4c2}{8c2}\) = \(\frac{3}{7}\) > \(\frac{1}{10}\)
\(\frac{4c2}{8c2}\) = \(\frac{3}{14}\) > \(\frac{1}{3}\) = No

let's say n (> 35) = 6 & n1( <35 ) = 2

\(\frac{6c2}{8c2}\) + \(\frac{2c2}{8c2}\) = \(\frac{16}{28}\) > \(\frac{1}{10}\)
\(\frac{6c2}{8c2}\) = \(\frac{15}{28}\) > \(\frac{1}{3}\) = yes