Fatima Hasan said:Homework Statement
One engineering group consists of 5 men and 7 women .
If 2 women refuse to be on the same team together , how many different project teams can be formed consisting of 2 men and 7 women ?
Homework Equations
-
The Attempt at a Solution
5 C 2 * 5 C 3 + (2 C 1 * 5 C 2) = 120
Can somebody check my answer please ?
3 womenDick said:and you need 7 women in the team
Is this the original problem statement? I find it ambiguous. DoesFatima Hasan said:One engineering group consists of 5 men and 7 women .
If 2 women refuse to be on the same team together , how many different project teams can be formed consisting of 2 men and 7 women ?
7 is a typo .tnich said:how many different project teams can be formed consisting of 2 men and 7 women
Fatima Hasan said:7 is a typo .
my question is "How many different project teams can be formed consisting of 5 men and 2 women "
The first term is how many ways to choose 2 men (5C2).Dick said:Looking at your answer I would say it's "How many different project teams can be formed consisting of 5 men and 3 women" as you said in your first correction. If so your answer has correct parts. It looks like the first term is how many ways to choose the team excluding the 2 women who don't get along. The next term looks like the ways to choose the womens team with those two. But the second term doesn't have any choice of men!? It would really be best if you explained your thinking rather than me guessing it.
Fatima Hasan said:The first term is how many ways to choose 2 men (5C2).
The next term is how many ways to choose 3 women , either choosing 3 women without the 2 women who don't get along (5C3) or (+) choosing one women of them and (*) two others (2C1 * 5C2) .
The number of different teams that can be formed with a group of 10 people is 3,628,800. This can be calculated using the formula nCr = n! / (r!(n-r)!), where n is the total number of people and r is the number of people in each team.
Yes, the number of teams formed will change depending on the size of the group. As the group size increases, the number of teams that can be formed also increases. Similarly, as the group size decreases, the number of teams that can be formed decreases.
If there are 5 people in each team, the number of teams that can be formed will depend on the total number of people in the group. For example, with a group of 20 people, there will be 4 teams (20/5 = 4). With a group of 35 people, there will be 7 teams (35/5 = 7).
Theoretically, there is no limit to the number of teams that can be formed. As long as there are enough people in the group, teams can continue to be formed. However, in practical situations, there may be limitations such as time, resources, and the purpose of forming teams.
The number of teams formed can greatly impact the group dynamics. With a larger number of teams, there may be more competition and diversity of ideas. However, with a smaller number of teams, there may be more collaboration and a stronger sense of teamwork. It ultimately depends on the goals and dynamics of the group.