(a) A 5-digit number is to be formed from the seven digits \(1,2,3,5,6,8,9\). Each digit can only be used once. Find the number of different 5-digit numbers if:

(i) there are no restrictions, (ii) the number is divisible by \(5\), (iii) the number is greater than \(60000\), (iv) the number is greater than \(60000\) and even.

(b) Ranjit has \(25\) friends, of whom \(15\) are boys and \(10\) are girls. He can only invite \(7\) friends. Find the number of ways the friends can be selected if:

(i) there are no restrictions, (ii) only \(2\) of the \(7\) friends are boys, (iii) the \(25\) friends include a boy and his sister who cannot be separated.