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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.

[1]

[Total: 1]

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.

[2]

[Total: 2]

3 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.

[1]

[Total: 1]

4 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.

[1]

[Total: 1]
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5 360 different 4-digit numbers can be formed using the digits 1, 3, 4, 6, 7 and 9. Each digit is used once only
in any 4-digit number.

How many of these 4-digit numbers are even and greater than 6000?

[3]

[Total: 3]

6 There are 720 different 5-digit numbers that can be formed using the digits 1, 2, 3, 5, 7 and 8, if each digit
may be used only once in any number.

How many of these 5-digit numbers are even and greater than 30 000?

[4]

[Total: 4]
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7 The number of combinations of n items taken 3 at a time is 6 times the number of combinations of n items
taken 2 at a time. Find the value of the constant n.

[4]

[Total: 4]

8 In an examination, candidates must select 2 questions from the 5 questions in section A and select 4 questions
from the 8 questions in section B. Find the number of ways in which this can be done.

[2]

[Total: 2]

9 The digits of the number 6 378 129 are to be arranged so that the resulting 7-digit number is even. Find the
number of ways in which this can be done.

[2]

[Total: 2]
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10 Find how many different 5-digit numbers can be formed using five of the eight digits

1, 2, 3, 4, 5, 6, 7, 8 if each digit can be used once only.

[2]

[Total: 2]

11 The number of combinations of n items taken 3 at a time is 92n. Find the value of the constant n.

[4]

[Total: 4]

12 There are 360 different 4-digit numbers that can be formed using the digits 2, 3, 5, 7, 8 and 9, if each digit
may be used only once in any number.

How many of these numbers are odd and greater than 7000?

[4]