In A Group Of 6 Boys And 4 Girls, Four Children Are To Be Selected. I

1.	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 ?
Answer» 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 = (6C1×4C3) + (6C2×4C2) + (6C3×4C1)+(6C4) = (24+90+80+15) = 209. 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 = (6C1×4C3) + (6C2×4C2) + (6C3×4C1)+(6C4) = (24+90+80+15) = 209.

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 ?

Answer»

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 = (6C1×4C3) + (6C2×4C2) + (6C3×4C1)+(6C4)

= (24+90+80+15)

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 = (6C1×4C3) + (6C2×4C2) + (6C3×4C1)+(6C4)

= (24+90+80+15)

= 209.