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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 × 7 A1 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 7 P 2 × 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
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