Thread: combinations

A commitee of 6 is to be selected from 10 people of whom A and B are two. HOw many commitees can be formed excluding A if B is included

i have already solved the first part of this qs which was if A and B were both included and that came out to be 70, using combination formula
i really need help for the second part. the answer is 140 but i dont know how to get there ><""

and can someone help me with second half of question too?
In how many ways can a commitee of 3 men and 4 women be chosen from 6 men and 7 women? What proportion of these committees contain a particular man and 2 particular women?
ive worked out the first part which is 700 but i dont know the second half which is 1/7 T.T

thanks guyz for any help given !

Originally Posted by flyinhigh123

A commitee of 6 is to be selected from 10 people of whom A and B are two. HOw many commitees can be formed excluding A if B is included

i have already solved the first part of this qs which was if A and B were both included and that came out to be 70, using combination formula
i really need help for the second part. the answer is 140 but i dont know how to get there ><""

[snip]

A committee either contains B or it doesn't. If it does, then you're not allowed to have A. If it doesn't, then you can any of the remaining nine:

(Number of committees with B and not A) + (number of committees without B) = .

Originally Posted by flyinhigh123

[snip]
In how many ways can a commitee of 3 men and 4 women be chosen from 6 men and 7 women? What proportion of these committees contain a particular man and 2 particular women?
ive worked out the first part which is 700 but i dont know the second half which is 1/7 T.T

thanks guyz for any help given !

Similar to the other question. You need another 2 men from the remaining 5 and another 2 women from the remaining 5. So the total number is . Now divide this number by 700 to get the required proportion.

Hello, flyinhigh123!

A commitee of 6 is to be selected from 10 people of whom A and B are two.
How many commitees can be formed excluding A if B is included?

There are ten people: .

With no restrictions, there are: . possible committees.

But and will not serve together.
We will count the committees in which and are together.

Since and are already on the committee,
. . we must choose 4 more people from the remaining 8 people.
There are: . committees with both and


Therefore, there are: . committees
. . which do not have both and

This agrees with Mr. F's solution.

In how many ways can a commitee of 3 men and 4 women be chosen from 6 men and 7 women?
What proportion of these committees contain a particular man and 2 particular women?

This is Mr. F's solution . . . with baby-talk.


You are right: there are 700 possible committees with 3 men and 4 women.


There are six men: .
and seven women: .

Suppose man and women must be on the committee.

We must select 2 more men from
. . . and 2 more women from

There are: . ways.


So the proportion is: .

thank you so much for your help !
special thanks to Soroban for your clear and step by step explanation, you really helped me =D