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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 option 'B'. Can you explain this answer?
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To find the number of different ways to select four children from a group of 6 boys and 4 girls such that at least one boy should be there, we can use the concept of combinations.
Total number of ways to select four children from a group of 10 children (6 boys and 4 girls) is given by the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of children and r is the number of children to be selected.
In this case, we need to find the number of ways to select four children such that at least one boy should be there. This means we need to find the total number of ways to select four children minus the number of ways to select four girls only.
Number of ways to select four children from a group of 10 children (including boys and girls) is given by:
10C4 = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Number of ways to select four girls only from a group of 4 girls is given by:
4C4 = 4! / (4! * (4-4)!) = 4! / (4! * 0!) = 1
Therefore, the number of ways to select four children such that at least one boy should be there is:
210 - 1 = 209
Hence, the correct answer is option B) 209.
Total number of ways to select four children from a group of 10 children (6 boys and 4 girls) is given by the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of children and r is the number of children to be selected.
In this case, we need to find the number of ways to select four children such that at least one boy should be there. This means we need to find the total number of ways to select four children minus the number of ways to select four girls only.
Number of ways to select four children from a group of 10 children (including boys and girls) is given by:
10C4 = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210
Number of ways to select four girls only from a group of 4 girls is given by:
4C4 = 4! / (4! * (4-4)!) = 4! / (4! * 0!) = 1
Therefore, the number of ways to select four children such that at least one boy should be there is:
210 - 1 = 209
Hence, the correct answer is option B) 209.
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