| Date | May 2012 | Marks available | 3 | Reference code | 12M.2.hl.TZ1.3 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | In how many | Question number | 3 | Adapted from | N/A |
Question
A team of 6 players is to be selected from 10 volleyball players, of whom 8 are boys and 2 are girls.
In how many ways can the team be selected?
In how many of these selections is exactly one girl in the team?
If the selection of the team is made at random, find the probability that exactly one girl is in the team.
Markscheme
\(\left( {\begin{array}{*{20}{c}}
{10} \\
6
\end{array}} \right) = 210\) (M1)A1
[2 marks]
\(2 \times \left( {\begin{array}{*{20}{c}}
8 \\
5
\end{array}} \right) = 112\) (M1)A1A1
Note: Accept \(210 - 28 - 70 = 112\)
[3 marks]
\(\frac{{112}}{{210}}\,\,\left( { = \frac{8}{{15}} = 0.533} \right)\) (M1)A1
[2 marks]
Examiners report
Most candidates answered this question well although in some cases candidates were not able to distinguish the use of permutations from combinations. Almost all candidates scored the two marks of part (c), but many of these were follow through marks.
Most candidates answered this question well although in some cases candidates were not able to distinguish the use of permutations from combinations. Almost all candidates scored the two marks of part (c), but many of these were follow through marks.
Most candidates answered this question well although in some cases candidates were not able to distinguish the use of permutations from combinations. Almost all candidates scored the two marks of part (c), but many of these were follow through marks.
