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Date November 2019 Marks available 3 Reference code 19N.2.AHL.TZ0.H_8
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Determine Question number H_8 Adapted from N/A

Question

Eight boys and two girls sit on a bench. Determine the number of possible arrangements, given that

the girls do not sit together.

[3]
a.

the girls do not sit on either end.

[2]
b.

the girls do not sit on either end and do not sit together.

[3]
c.

Markscheme

METHOD 1

10!2×9!(=2903040)            (A1)(A1)A1

Note: Award A1 for 10!A1 for 2×9!A1 for final answer.

 

METHOD 2

9×8×8!            (A1)(A1)A1

Note: Award A1 for 9×8 or equivalent, A1 for 8! and A1 for answer.

 

[3 marks]

a.

METHOD 1

8×7×8!(=2257920)           (A1)A1

Note: Award (A1) for 8×7A1 for final answer.

 

METHOD 2

10!2×8!2×2×7×8!

Note: Award A1 for 10! minus EITHER subtracted terms and A1 for final correct answer.

 

[2 marks]

b.

METHOD 1

8×7×(8!2×7!)(=1693440)          (A1)(A1)A1

Note: Award (A1) for 8×7, (A1) for 2×7!A1 for final answer. (8!2×7!) can be replaced by 6×7! or 7P2×6! which may be awarded the second A1.

 

METHOD 2

their answer to (a) 2×8!2×2×7×8!          (A1)(A1)A1

Note: Award A1 for subtracting each of the terms and A1 for final answer.

 

METHOD 3

their answer to (b) 2×7×8! or equivalent          (A1)A2

Note: Award A1 for the subtraction and A2 for final answer.

 

[3 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 1—Number and algebra » SL 1.9—Binomial theorem where n is an integer
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Topic 1—Number and algebra » AHL 1.14—Complex roots of polynomials, conjugate roots, De Moivre’s, powers & roots of complex numbers
Topic 1—Number and algebra

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