CAIE S1 2014 November — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2014
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicPermutations & Arrangements
TypeSelection with type constraints
DifficultyEasy -1.2 This is a straightforward application of combinations with constraints. Once students recognize that 2 positions are fixed (president and treasurer must go), they simply need to choose 43 from the remaining 48 members using C(48,43). It requires only basic understanding of combinations and one simple calculation, making it easier than average.
Spec5.01b Selection/arrangement: probability problems

The 50 members of a club include both the club president and the club treasurer. All 50 members want to go on a coach tour, but the coach only has room for 45 people. In how many ways can 45 members be chosen if both the club president and the club treasurer must be included? [3]

AnswerMarks Guidance
\(^{18}C_{43} = 1712304 (1710000)\)B1, B1, B1 3 48 seen in a single term combination or 43 or 5 seen in a single term combination or Both can be mult by integer \(k \geq 1\) or Correct final answer
$^{18}C_{43} = 1712304 (1710000)$ | B1, B1, B1 3 | 48 seen in a single term combination or 43 or 5 seen in a single term combination or Both can be mult by integer $k \geq 1$ or Correct final answer

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The 50 members of a club include both the club president and the club treasurer. All 50 members want to go on a coach tour, but the coach only has room for 45 people. In how many ways can 45 members be chosen if both the club president and the club treasurer must be included? [3]

\hfill \mbox{\textit{CAIE S1 2014 Q1 [3]}}