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?  Choose the correct choice from the following:
A) 159  B) 194  C) 205  D) 209  E) None of these
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 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + 6C4   = (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + 6C2   = (6 x 4) +[(6x5)/(2x1) x (4x3)/(2x1)] + [(6x5x4)/(3x2x1)) x 4] +[(6x5)/(2x1)]   = 24 + 90 + 80 + 15= 
<gadget id="calculator">24 + 90 + 80 + 15</gadget>
<output>209</output>
209   Answer 209.
<result>D</result>
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?