(i) no girl
Table for computing the number of ways of selections.
| Girls (out of 4) |
Boys (out of 7) |
Number of ways |
| 0 |
5 |
4C0 x 7C5 |
∴ Required number of ways = 4C0 x 7C5
= 1 x 7C2 = (7 x 6)/(2 x 1) = 21
(ii) at least 3 girls
| Girls (out of 4) |
Boys (out of 7) |
Number of ways |
| 3 |
2 |
4C3 x 7C2 |
| 4 |
1 |
4C4 x 7C1 |
(iii) at least one boy and one girl
| Girls (out of 4) |
Boy (out of 7) |
Number of way |
| 1 |
4 |
4C1 x 7C4 = 140 |
| 2 |
3 |
4C2 x 7C3 = 210 |
| 3 |
2 |
4C3 x 7C2 = 84 |
| 4 |
1 |
4C4 x 7C1 = 07 |
∴ Required numbers of ways
= 140 + 210+84 + 07 = 441
