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 option:  A) 210  B) 209  C) 212  D) 211  E) 200
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 options 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 × 4C1   We can select 2 boys and 2 girls ...(option 3)   Number of ways to this = 6C2 × 4C2   We can select 1 boy and 3 girls ...(option 4)   Number of ways to this = 6C1 × 4C3   Total number of ways   = 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3   = 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]   = 15 + 80 + 90 + 24= 
<gadget id="calculator">15 + 80 + 90 + 24</gadget>
<output>209</output>
209   209
<result>B</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?