Out of a class of 8 boys and 4 girls, a group of 7 people is chosen at random.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [B1] Seen as denominator of fraction (Total number of selections = 12C7= 792)
2. [M1] Correct unsimplified expression for selections with boy included seen as numerator of fraction (Selections with boy included = 11C6 or 12C7 – 11C7 = 462)
3. [A1] Correct answer (462/792 = 7/12 (0.583))
4. [B1] One unsimplified product correct (Method 1)
5. [M1] No of selections (products of Cr and Pr) added for 2, 3 and 4 girls with no of girls and no of boys summing to 7 (Method 1)
6. [A1] Correct total (Method 1)
7. [A1ft] Correct answer 'total'/( 'total no of selections' from i) (Method 1)
8. [B1] One unsimplified no of selections correct (Method 2)
9. [M1] No of selections (products of Cr and Pr) added for 0 and 1 girls with no of girls and no of boys summing to 7 (Method 2)
10. [A1] 792 – 120 = 672 or 1 – 120/792 (Method 2)
11. [A1ft] '672' over '792' from i (Method 2)