How many committees of 4 members can be formed from 9 people?

A

)

126

different committees

B

)

21

different committees

C

)

70

different committees

Explanation:Explanation:

Recall: The number of different ways of arranging

n

numbers is

n

!

If 4 people are to be selected from 9 people:

There are 9 different choices for the first person.

There are 8 different choices for the second person.

There are 7 different choices for the third person.

There are 6 different choices for the fourth person.

This gives

9

×

8

×

7

×

6

different committees, however this will include the same combinations of people.

There are

4

×

3

×

2

×

1

ways in which 4 people can be chosen.

A) Therefore, for 4 people chosen from 9 there are

9

×

8

×

7

×

6

×

5

4

×

3

×

2

×

1

=

126

different committees.

B) If two people must stand, there are 2 people to be chosen from the remaining 7. Applying the same thinking as above this gives:

7

×

6

2

=

21

different committees.

C) if either one or the other must stand there are then 3 people who must be chosen from the remaining

7

people;

7

×

6

×

5

3

×

2

×

1

=

35

But this can happen in 2 different ways, depending on whether John or Barbara are on the committee.

So,

2

×

35

=

70

different committees can be formed.

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