3. (a) A non-case-sensitive password comprising of 3 digits and 4 alphabets needs to be
formed from digits 2, 5, 6, 7, 8, and alphabets a, b, d, e, f, i,. With a condition that the digits and the alphabets can only be used once, how many passwords can be formed if i.
it can only contain even numbers.
[3 marks]
ii. the alphabets and the numbers are in alternate order.
[3 marks]
iii. the numbers must be put together.
[4 marks]
(b) There are 4 male and 5 female students in a Mathematics club. A team of 4 students will be chosen to represent the club for a local Mathematics competition. In how many ways can the team be formed if
i. anyone can be chosen to represent the club.
[1 marks]
ii. one particular student must be selected.
[2 marks]
ili. it must have equal number of male and female students.
[2 marks]