Data management
posted by Emily .
The camera club has 5 members, and the math club has 8 members. There is only one member common to both clubs. In how many ways could a committee of 4 people be formed with at least 1 member from each group?

Let's say Bob is in both clubs. There are 11 other people.
Two cases: Bob is on the committee, or not:
a) Bob included:
First choose him, then choose any 3 of the other 11, since both clubs are represented by Bob:
11C3 ways to do that.
b) Bob excluded:
Now start with 11C4 (committees made up of the other 11 people).
Subtract 4C4 = 1 way with all 4 others from the camera club,
and 7C4 = 35 ways with 4 others from the math club.
11C3 + 11C4  1  7C4 = 165 + 330  1  35 = 459
Or we could say:
there are 12C4 total committees ( = 495 = 165 + 300 )
not worrying about Bob, and then just subtract the 1 which is the 4 camera club members
who are not Bob and the 35, which is the same for the math club.
Respond to this Question
Similar Questions

Algebra
Club R has 11 members and Club T has 16 members. If a toatal of 20 people belong to the two clubs, how many people belong to both clubs? 
Algebra 2
Club R has 11 members and club T has 16 members. If a total of 20 people belong to the two clubs, how many people belong to both clubs? 
Math
A club of 10 members is to select 3 officers (president, vicepresident and secretary). In how many ways can they do this? 
algebra
Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently … 
algebra
Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently … 
Combination math
The camera club has 5 members and the mathematics club has 8. There is only one member common to both clubs. In how many ways could a committee be formed with at least one member from each club? 
Math
The ratio of boys to girls in the checkers club at one school is 2:3. the number of club members is more than 20 and fewer than 30. how many club members are there? 
Matrix
Urban population between n and m is the number of members of the club each club the number of members of both clubs even prove m <n 
math help
In 2011 a spots club offers its members three types of activities: volleyball basketball and tennis. Each member practices only one of the three activities:30% of the members practice volleyball, 20% of the members practice basketball, … 
math
in a grade 7 class, 36 students are either members of the math club or science club or both. 10 students are members of both clubs. if 31 students are members of the math club how many are members of the science club?