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)159b)209c)201d)212Correct answer is option 'B'. Can you explain this answer?
Ref: https://edurev.in/question/471143/In-a-group-of-6-boys-and-4-girls-four-children-are-to-be-selected-In-how-many-different-ways-can-t
In a group of 6 boys and 4 girls, four children are to be selected such that
at least one boy should be there.
Hence we have 4 choices as given below
We can select 4 boys ------(Option 1).
Number of ways to this = 6C4
We can select 3 boys and 1 girl ------(Option 2)
Number of ways to this = 6C3 x 4C1
We can select 2 boys and 2 girls ------(Option 3)
Number of ways to this = 6C2 x 4C2
We can select 1 boy and 3 girls ------(Option 4)
Number of ways to this = 6C1 x 4C3
Total number of ways
= (6C4) + (6C3 x 4C1) + (6C2 x 4C2) + (6C1 x 4C3)
= (6C2) + (6C3 x 4C1) + (6C2 x 4C2) + (6C1 x 4C1) [Applied the formula nCr = nC(n - r) ]
=[6×52×1]+[(6×5×43×2×1)×4]+[(6×52×1)(4×32×1)]+[6×4]=[6×52×1]+[(6×5×43×2×1)×4]+[(6×52×1)(4×32×1)]+[6×4]
= 15 + 80 + 90 + 24
= 209
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