1.3: 4-digit numbers and medical committee
(a)(i)[1]
Find how many different 4-digit numbers can be formed using the digits 1, 3, 4, 6, 7 and 9. Each digit may be used once only in any 4-digit number.
(a)(ii)[3]
How many of these 4-digit numbers are even and greater than 6000?
(b)(i)[1]
A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if there are no restrictions.
(b)(ii)[2]
A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if the committee contains at least one doctor.
(b)(iii)[1]
A committee of 5 people is to be formed from 6 doctors, 4 dentists and 3 nurses. Find the number of different committees that could be formed if the committee contains all the nurses.