Form Team of 4 Boys with No More than 1: Combination Problem

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In summary, the question asks for the number of ways to choose a team of four from a group of 5 boys and 8 girls, where the team contains no more than one girl. By fixing one girl and calculating the number of combinations for 3 boys, which is 10, and multiplying that by 8, we get 80. However, since the question also allows for a team with no girls, we must add the number of combinations for all boys, which is 5, resulting in a total of 85 possible teams.
  • #1
Taylor_1989
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A group consists of 5 boys and 8 girls. In how many ways can a team of four boys be chosen, if the team contains.

no more than one boy

So my attempt was this. I thought to myself well if I fix one girl and calculate the number on combination 5 boys can be chosen for 3 spaces which is 10, I would then multiply that by 8 to get the ans. So my ans comes out to be 80 , but the ans in back to the book comes out to be 85 any thoughts?

Big thanks in advance.
 
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  • #2
A team of four boys with no more than one boy makes no sense.
 
  • #3
PeroK said:
A team of four boys with no more than one boy makes no sense.
My bad I ment no more than one girl. I was looking at the question below when typing this.
 
  • #4
Taylor_1989 said:
My bad I ment no more than one girl. I was looking at the question below when typing this.
A team of four boys has no girls in it!

Do you mean a team of four with no more than one girl?
 
  • #5
PeroK said:
A team of four boys has no girls in it!

Do you mean a team of four with no more than one girl?
yes. Let me re write the question.

A group consists of 5 boys and 8 girls. In how many ways can a team of four be chosen, if the team contains

no more than one girl.
 
  • #6
Taylor_1989 said:
yes. Let me re write the question.

A group consists of 5 boys and 8 girls. In how many ways can a team of four be chosen, if the team contains

no more than one girl.
So, the team might have no girls in it?
 
  • #7
Ah I don't know if you ask that question to lead me to the ans or it as an actual question, but I just realized what the question is asking me. So there is 80 combinations of having 1 girl on the team but the questions ask for no more therefore I would have to include the number of combinations for all boys i.e 5 so 80+5=85
 
  • #8
That looks like the missing 5 teams in any case!
 
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1. How many different combinations of 4 boys can be formed from a group of 10 boys?

There are 210 different combinations of 4 boys that can be formed from a group of 10 boys. This can be calculated using the combination formula: nCr = n!/(r!(n-r)!), where n is the total number of boys and r is the number of boys in each combination.

2. Can we form a team of 4 boys if there are only 3 boys available?

No, it is not possible to form a team of 4 boys if there are only 3 boys available. The number of boys in the team must be less than or equal to the total number of boys available.

3. Can we have more than one team of 4 boys from a group of 10 boys?

Yes, it is possible to have multiple teams of 4 boys from a group of 10 boys. In fact, there can be a total of 210 different teams of 4 boys that can be formed from a group of 10 boys.

4. Is it necessary to have exactly 4 boys in each team?

No, it is not necessary to have exactly 4 boys in each team. The problem states that the team can have no more than 4 boys, but it can also have less than 4 boys. For example, a team can have 2 or 3 boys as well.

5. How does the order of the boys in the team affect the total number of combinations?

The order of the boys in the team does not affect the total number of combinations. For example, if the team consists of boys A, B, C, and D, it is considered the same combination as a team consisting of boys B, A, C, and D.

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