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In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
- a)159
- b)209
- c)201
- d)212
Correct answer is 'B'. Can you explain this answer?
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Verified Answer
In a group of 6 boys and 4 girls, four children are to be selected. In...
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways = (6C1*4C3)+(6C2*4C2)+(6C3*4C1)+6C4
= (6C1*4C1)+(6C2*4C2)+(6C3*4C1)+6C2 = 209.
Most Upvoted Answer
In a group of 6 boys and 4 girls, four children are to be selected. In...
To solve this problem, we need to use the concept of complementary counting. We can count the total number of ways to select four children from a group of 10, and then subtract the number of ways to select four girls from the group.
Total number of ways to select 4 children from a group of 10 = 10C4 = 210
Number of ways to select 4 girls from a group of 4 = 4C4 = 1
Therefore, the number of ways to select four children such that at least one boy is there = 210 - 1 = 209.
Hence, the correct answer is option B (209).
Total number of ways to select 4 children from a group of 10 = 10C4 = 210
Number of ways to select 4 girls from a group of 4 = 4C4 = 1
Therefore, the number of ways to select four children such that at least one boy is there = 210 - 1 = 209.
Hence, the correct answer is option B (209).
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Community Answer
In a group of 6 boys and 4 girls, four children are to be selected. In...
In the above question we can have (3 girls and 1boy),(2girls and 2boys),(1girl and three boys),(0 girls and 4boys).
(6C3*4C1)+(6C2*4C2)+(6C1*4C3)+(6C0*4C4)
so the answer therefore gives us *209*
(6C3*4C1)+(6C2*4C2)+(6C1*4C3)+(6C0*4C4)
so the answer therefore gives us *209*
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