(a)[4]
Find the number of distinct arrangements of all nine letters in PINEAPPLE if no vowel $(A, E, I)$ is placed beside another vowel.
(b(i))[2]
One country’s cricket squad has 16 players, made up of 7 batsmen, 5 bowlers, 2 all-rounders and 2 wicket-keepers. The manager selects an 11-player team containing 5 batsmen, 4 bowlers, 1 all-rounder and 1 wicket-keeper. Find the number of different teams the manager can choose.
(b(ii))[3]
Find the number of different teams the manager can choose if one particular batsman will not be in the team whenever one particular bowler is in the team.