Find the number of different ways in which the 10 letters of the word SHOPKEEPER can be arranged so that the Ps are not next to each other. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_51 Year：2020 Question No：7(b)

Answer:

Total number of ways: \(\frac{10 !}{2 ! 3 !}(=302400)\) (A)
With Ps together: \(\frac{9 !}{3 !}(=60480)(B)\)
With Ps not together: \(302400-60480\)
241920
Alternative method for question 7 (b)
\(\frac{8 !}{3 !}\)
\(\times \frac{9 \times 8}{2}\)
241920

Knowledge points:

5.2.2.1 repetition (e.g. the number of ways of arranging the letters of the word ‘NEEDLESS’)

5.2.2.2 restriction (e.g. the number of ways several people can stand in a line if two particular people must, or must not, stand next to each other). (Questions may include cases such as people sitting in two (or more) rows.) (Questions about objects arranged in a circle will not be included.)

Answer:

Knowledge points:

Solution:

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