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. 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) + 6 x 5 x 4 x 3 + 6 x 5 x 4 x 4 + 6 x 5
  2 x 1 2 x 1 3 x 2 x 1 2 x 1
  = (24 + 90 + 80 + 15)
  = 209.
• 12 years agoHelpfull: Yes(11) No(8)
• total=10C4
  all r girls=4C4
  the ans is 10C4-4c4=209
  
• 11 years agoHelpfull: Yes(8) No(2)
• (at least)=Total-None
  10c4 - 4c4
  =210-1
  =209
• 5 years agoHelpfull: Yes(0) No(0)