Question:
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is
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“At least one” problems are best solved using complement method.
Updated On: May 1, 2026
- \( 159 \)
- \( 209 \)
- \( 200 \)
- \( 240 \)
- \( 212 \)
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
Use complement counting.
Step 1: Total ways to choose 4 from 10.
\[ \binom{10}{4} = 210 \]
Step 2: Count teams with no boys (all girls).
\[ \binom{4}{4} = 1 \]
Step 3: Subtract invalid cases.
\[ 210 - 1 = 209 \]
Step 4: Interpret result.
All valid teams have at least one boy.
Step 5: Final answer.
\[ 209 \]
Step 1: Total ways to choose 4 from 10.
\[ \binom{10}{4} = 210 \]
Step 2: Count teams with no boys (all girls).
\[ \binom{4}{4} = 1 \]
Step 3: Subtract invalid cases.
\[ 210 - 1 = 209 \]
Step 4: Interpret result.
All valid teams have at least one boy.
Step 5: Final answer.
\[ 209 \]
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