A group of 9 workers decides to send a delegation of 3 to their supervisor to dicusss their grievences.
c.) If there are 4 women and 5 men in the group, how many delegations would include at least 1 women?
iS THIS CORRECT:
C(4,1)xC(5,1)+C(4,3)XC(5,0)=24
The number of possible delegations without considering any restriction is C(9,3) = 84.
The number of possible delegations which do not include any woman is C(5,3) = 10.
So the answer should be: 84-10 = 74.
I don't know how you get 129, and why is the answer 112. If you write your solution, I could check it to find the flaw (or maybe my solution is flawed).
? · 5 years ago
There are 9 of them so a delegation of 3 can go in 9C3 = 84 ways. There are 5 men in them so "all men" delgations will be 5C3= 10.
hence 84-10 = 74 delegations will contain at least one lady.
So what you have done and heard, both are wrong.
74 is correct.
Yes, your approach and calculation are correct. To calculate the number of delegations that include at least 1 woman, you need to consider two scenarios:
Scenario 1: 1 woman and 1 man are selected for the delegation. In this case, you need to calculate the combination of selecting 1 woman from the 4 available women (C(4,1)), multiplied by the combination of selecting 1 man from the 5 available men (C(5,1)).
Scenario 2: 3 women are selected for the delegation. In this case, you need to calculate the combination of selecting 3 women from the 4 available women (C(4,3)), multiplied by the combination of selecting 0 men from the 5 available men (C(5,0)).
Then, you add the results of both scenarios to get the total number of delegations that include at least 1 woman.
So, the calculation would be: C(4,1) * C(5,1) + C(4,3) * C(5,0) = 24.