Homework Help: Discrete Math

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 - There were 40 members in a hockey club. 3/8 of them were girls. When ...
gr12 math - froma group of 6 ladies and 4 men, determine in how many ways a ...
math - from a group of women and 4 men, determine in how many ways a committee ...
statistics - a sample of 120 men and women randomly divided into 3 groups with ...
psychology - A typical act of servant leader should be to: a) work for salary no...
psychology - A typical act of servant leader should be to: a) work for salary no...

For Further Reading

First Name:
School Subject:
Answer: