data management gr.12
posted by Anonymous .
In how many ways can a committee of 8 members be chosen from 7 males and 9 females if the committee must contain at least 3 males?
Please verify if my solution is correct:
total# of 8 members 16C8
#with NO males 7C8
# with at least 3 males
(7C3 x 4C2)+ (7C4 x 4C1)+(7C5 x9C0)
Thanks in advance

I would like to see, in your interpretation, what each of the expressions mean.
(7C3 x 4C2)
(7C4 x 4C1)
(7C5 x9C0) 
(7C3 x4C2) # ways of choosing committee 3 males + 5 females. I made a mistake, I think it should be 9C5 instead of 4C2 => (7C3 x 9C5)
(7C4 x 9C4) choosing 4 males + 4 females (again I made a mistake)
Thanks 
ok, that sounds reasonable.
If you like, you can continue with your method, which is
(7C3*9C5)+(7C4*9C4)+(7C5*9C3)+(7C6*9C2)+(7C7*9C1)
or, equivalently,
16C8(7C0*9C8+7C1*9C7+7C2*9C6)
which gives (or should give) the same result above.
In doing counting problems, it is always wise to try two different ways of counting the same objective to check the calculations.
Respond to this Question
Similar Questions

Math (Data Management)
The student council is ordering pizza for their next meeting. There are 20 council members, 7 of whom are vegetarian. A committee of 3 will order 6 pizzas from a pizza shop that has a special price for large pizzas with up to three … 
College Math
Assume that you have a total of 13 people on the committee: 4 black males, 4 black females, 1 white male, and 4 white females. Party rules require that at least one black and at least one female hold one of the three offices. In how … 
Data management!! [ Hi economyst] Please Help.
Hi. economyst. Thanks for your help with my other questions. But I am still stuck with this question: @@@@My question: Rain is an amazing singer, but cannot play any instruments. He desperately wants a rock band that has a drummer, … 
Finite Math
Assume that you have a total of 15 people on the committee: 5 black males, 5 black females, 1 white male, and 4 white females. Party rules require that at least one black and at least one female hold one of the three offices. In how … 
College Finite
Assume that you have a total of 9 people on the committee: 2 black males, 1 black female, 1 white male, and 5 white females. Party rules require that at least one black and at least one female hold one of the three offices. In how … 
maths
A committee of 4 people is to be chosen from 5 married coiples.find in how many ways the committee can be chosen if: i) everyone is equallt eligible ii) the committee should include at least one woman solution so far.5 couples=10 people. … 
Maths
From a group of 10 people, 5 men and 5 women, six are to be chosen to serve on a committee. a) In how many ways can the committee be chosen? 
maths
A committee of 4people is to be chosen from 5 married couples. Find in how many ways the committee can be chosen if; 1) everyone is equally eligible. 2) the committee should include at least one woman 
Math
A cooperation must appoint a president, CEO, COO,and a CFO. It must also appoint a planning committee with 3 different members. There are 15 candidates and officers can also serve on the planning committee. How many different ways … 
math
A committee of 5 is chosen from 6 teachers and 3 students and 7 others. Determine the number of ways of selecting the committee if it is to contain: (a)at least two teachers (b)no teacher nor student