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In a group of five boys and five girls, 3 persons are to be selected for a competition. What is the probability that all three persons are girls?
- a)2/12
- b)1/12
- c)3/12
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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In a group of five boys and five girls, 3 persons are to be selected f...
Required Probability 
Most Upvoted Answer
In a group of five boys and five girls, 3 persons are to be selected f...
Probability will be
[5!÷(3!×2!)]÷[10!÷(7!×3!)]
=10÷120
=1÷12
Explanation
For selection combinations is used
correctly it is written as
5 10
C ÷ C
3 3
because if 3 girls are selected they are selected from group of 5 girls and then in whole group of 10 people
[5!÷(3!×2!)]÷[10!÷(7!×3!)]
=10÷120
=1÷12
Explanation
For selection combinations is used
correctly it is written as
5 10
C ÷ C
3 3
because if 3 girls are selected they are selected from group of 5 girls and then in whole group of 10 people
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In a group of five boys and five girls, 3 persons are to be selected f...
Solution:
Total number of ways to select 3 persons out of 10:
- The total number of ways to select 3 persons out of 10 (5 boys and 5 girls) is given by 10C3 = 120.
Total number of ways to select 3 girls:
- The total number of ways to select 3 girls out of 5 is given by 5C3 = 10.
Probability of selecting all three girls:
- The probability of selecting all three girls out of 10 is given by the number of ways to select 3 girls divided by the total number of ways to select 3 persons.
- Therefore, the probability = 10/120 = 1/12.
Therefore, the correct answer is option B) 1/12.
Total number of ways to select 3 persons out of 10:
- The total number of ways to select 3 persons out of 10 (5 boys and 5 girls) is given by 10C3 = 120.
Total number of ways to select 3 girls:
- The total number of ways to select 3 girls out of 5 is given by 5C3 = 10.
Probability of selecting all three girls:
- The probability of selecting all three girls out of 10 is given by the number of ways to select 3 girls divided by the total number of ways to select 3 persons.
- Therefore, the probability = 10/120 = 1/12.
Therefore, the correct answer is option B) 1/12.
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