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 ?

We may have (1 boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or(4 boys).

Required number of ways = ( $C16\times C34$) +  $C26\times C24$  + ( $C36\times C14$) + ( $C46$)  

= (24+90+80+15) 

= 209.