Answer: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.