Find the number of different arrangements that can be made from the 9 letters of the word JEWELLERY in which the two Ls are not next to each other. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_51 Year：2020 Question No：2(b)

Answer:

Total number: \(\frac{9 !}{3 ! 2 !}(30240)\)
Number with Ls together \(=\frac{8 !}{3 !}(6720)\)
Number with Ls not together \(=\frac{9 !}{3 ! 2 !}-\frac{8 !}{3 !}\)
\(=30240-6720\)
23520
Alternative method for question 2(b)
\(\frac{7 !}{3 !} \times \frac{8 \times 7}{2}\)
\(7 ! \times k\) in numerator, \(k\) integer \(\geq 1\)
\(8 \times 7 \times m\) in numerator or \(8 \mathrm{C} 2 \times m, m\) integer \(\geq 1\)
3 ! in denominator
23520

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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