Date | November 2020 | Marks available | 3 | Reference code | 20N.2.AHL.TZ0.H_7 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Determine | Question number | H_7 | Adapted from | N/A |
Question
At a gathering of 12 teachers, seven are male and five are female. A group of five of these teachers go out for a meal together. Determine the possible number of groups in each of the following situations:
There are more males than females in the group.
Two of the teachers, Gary and Gerwyn, refuse to go out for a meal together.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
identifying two or three possible cases (M1)
total number of possible groups is (75)+(74)(51)+(73)(52) (A1)(A1)
Note: Award A1 for any two correct cases, A1 for the other one.
=21+(35×5)+(35×10)
=546 A1
[4 marks]
METHOD 1
identifying at least two of the three possible cases- Gary goes, Gerwyn goes or neither goes (M1)
total number of possible groups is (105)+(104)+(104) (A1)
=252+210+210
=672 A1
METHOD 2
identifying the overall number of groups and no. of cases where both Gary and Gerwyn go. (M1)
total number of possible groups is (125)-(103) (A1)
=792-120
=672 A1
[3 marks]