3.9: Six-character passwords and a combinations relation

0606/12/M/J/21 — Question 7 · 8 marks

A six-character password is to be made from the following eight characters.
Digits: 1, 3, 5, 8, 9
Symbols: ∗*, $\text{\$}, #\#
No character may be used more than once in a password.
(a)(i)
Find the number of different passwords that can be chosen if there are no restrictions.
[1]
(a)(ii)
Find the number of different passwords that can be chosen if the password starts with a digit and finishes with a digit.
[2]
(a)(iii)
Find the number of different passwords that can be chosen if the password starts with three symbols.
[2]
(b)
The number of combinations of 5 objects selected from nn objects is six times the number of combinations of 4 objects selected from n−1n - 1 objects. Find the value of nn.
[3]