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Date May 2021 Marks available 3 Reference code 21M.2.AHL.TZ2.7
Level Additional Higher Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number 7 Adapted from N/A

Question

Eight runners compete in a race where there are no tied finishes. Andrea and Jack are two of the eight competitors in this race.

Find the total number of possible ways in which the eight runners can finish if Jack finishes

in the position immediately after Andrea.

[2]
a.

in any position after Andrea.

[3]
b.

Markscheme

Jack and Andrea finish in that order (as a unit) so we are considering the arrangement of 7 objects               (M1)

7! =5040 ways                      A1

 

[2 marks]

a.

METHOD 1

the number of ways that Andrea finishes in front of Jack is equal to the number of ways that Jack finishes in front of Andrea            (M1)

total number of ways is 8!                   (A1)

8!2 =20160  ways             A1

 

METHOD 2

the other six runners can finish in 6! =720 ways               (A1)

when Andrea finishes first, Jack can finish in 7 different positions

when Andrea finishes second, Jack can finish in 6 different positions etc

7+6+5+4+3+2+1 (=28) ways             (A1)

hence there are (7+6+5+4+3+2+1)×6! ways

28×6! (=20160) ways              A1

 

[3 marks]

b.

Examiners report

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

Syllabus sections

Topic 1—Number and algebra » AHL 1.10—Perms and combs, binomial with negative and fractional indices
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Topic 1—Number and algebra

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