3.29: 6-digit numbers and a mixed committee
(a)(i)[1]
A 6-digit number is to be formed using the digits 0–9, each at most once, and cannot start with 0. Find how many 6-digit numbers can be formed.
(a)(ii)[3]
Find how many of these 6-digit numbers are divisible by 5.
(b)(i)[1]
A committee of 7 people is to be chosen from 6 doctors, 10 nurses and 8 dentists. Find the number of committees that can be chosen.
(b)(ii)[1]
Find the number of committees that can be chosen if all the doctors have to be on the committee.
(b)(iii)[2]
Find the number of committees that can be chosen if there has to be at least one dentist on the committee.