A-LevelMathematicsProbability and statistics9709/62 · May/June 2017 · Q69 Marks
A library contains 4 identical copies of book A, 2 identical copies of book B and 5 identical copies of book C. These 11 books are arranged on a shelf in the library.
- (i)Calculate the number of different arrangements if the end books are either both book A or both book B.[4]
- (ii)Calculate the number of different arrangements if all the books A are next to each other and none of the books B are next to each other.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- (*M1 Considering AA and BB options with values
- A1 Any one option correct
- DM1 Summing their AA and BB outcomes only
- A1)
- (*M1 Considering all As together – 8! seen alone or as numerator – condone × 4! for thinking A's not identical
- M1 Considering all As together and all Bs together – 7! seen alone or numerator
- M1 Removing repeated Bs or Cs – Dividing by 5! either expression or 2! 1st expression only – OE
- DM1 Subt their 42 from their 168 (dependent upon first M being awarded)
- A1)
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