Posted by **Justin** on Thursday, November 4, 2010 at 10:57am.

7.A group has 9 women and 7 men.

d. Suppose 2 members of the group refuse to work together. How many subgroups of 5 can be chosen

8. In how many ways can 16 people be seated:

a. In a row, if 4 of the 16 do not want to sit next to one another

b. In a row, if 3 of the 16 must be seated next to one another

c. In a circle, if 3 of the 16 must be seated next to one another.

d. In a circle, if 4 of the 16 do not want to sit next to one another.

- Discrete Math -
**MathMate**, Thursday, November 4, 2010 at 11:40am
I'll tackle 7d.

Out of 7 people, two do not want to work together.

Method 1:

Calculate all possible ways (5 out of 7), and subtract those that include the two particular persons (3 out of 5).

C(7,5)-C(5,3)

=7!/(5!2!)+5!/(3!2!)

=11

Method 2:

Make 3 cases,

1. without A, nor B : 1 way

2. with only A and not B:

C(5,4)=5

3. with only B and not A:

C(5,4)=5

Total: 1+5+5=11

## Answer This Question

## Related Questions

- Discrete Math - 7.A group has 9 women and 7 men. d. Suppose 2 members of the ...
- discrete math - Suppose that a department contains 10 men and 17 women. How many...
- discrete math - Suppose that a department contains 10 men and 17 women. How many...
- math - a class consists of 14 men and 16 women. A group of 5 is randomly chosen ...
- Maths - From a group of 10 people, 5 men and 5 women, six are to be chosen to ...
- gr12 math - froma group of 6 ladies and 4 men, determine in how many ways a ...
- Discrete Math - 3. A club with 8 women and 6 men needs to choose two different ...
- math - from a group of women and 4 men, determine in how many ways a committee ...
- Math - 2. Three members of a 12 person singing group are going to be chosen to ...
- Math (probability) - Three members of a 12 person singing group are going to be ...

More Related Questions