2.14: Even 5-digit numbers and seating arrangements
(a)(i)[2]
Find how many 5-digit even numbers can be made using each of the digits 1, 2, 3, 4, 5 once only.
(a)(ii)[2]
Find how many different 3-digit numbers can be made using the digits 1, 2, 3, 4, 5 if each digit can be used once only.
(b)(i)[2]
A man and two women are to sit in a row of five empty chairs. Calculate the number of ways they can be seated if the two women must sit next to each other.
(b)(ii)[2]
A man and two women are to sit in a row of five empty chairs. Calculate the number of ways they can be seated if all three people must sit next to each other.