There are 3 boys and 2 girls in team A, and 3 girls and 2 boys in team B. If 1 person is selected from each team, then the number of ways of selecting 1 boy and 1 girl is?
Understand the Problem
The question is asking for the number of ways to select one boy and one girl from two different teams, taking into account the specified number of boys and girls in each team. This involves using combinations to calculate the total possibilities.
Answer
$12$
Answer for screen readers
The total number of ways to select 1 boy and 1 girl is $12$.
Steps to Solve
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Identify the composition of each team Team A has 3 boys and 2 girls.
Team B has 2 boys and 3 girls. -
Calculate the combinations for selecting 1 boy and 1 girl from Team A From Team A, the number of ways to select 1 boy is:
$$ C(3, 1) = 3 $$ The number of ways to select 1 girl is:
$$ C(2, 1) = 2 $$ Thus, the total combinations from Team A are:
$$ 3 \times 2 = 6 $$ -
Calculate the combinations for selecting 1 boy and 1 girl from Team B From Team B, the number of ways to select 1 boy is:
$$ C(2, 1) = 2 $$
The number of ways to select 1 girl is:
$$ C(3, 1) = 3 $$
Thus, the total combinations from Team B are:
$$ 2 \times 3 = 6 $$ -
Calculate the total number of ways to select 1 boy and 1 girl from both teams Now, combine the selections from both teams:
Total selections = Selections from Team A + Selections from Team B
$$ 6 + 6 = 12 $$
The total number of ways to select 1 boy and 1 girl is $12$.
More Information
In this problem, we calculated the possible selections by using combination formulas for each team and then added the results. This method allows us to see all the different pairings of boys and girls across both teams.
Tips
- Forgetting to multiply the combinations for boys and girls within the same team instead of just adding them.
- Not considering both teams when calculating the total selections.
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