Question 2104

(a) Find the number of ways in which the letters of the word PERMUTATION{PERMUTATION} can be arranged if

(i) (1 mark) there are no restrictions,

(ii) (2 marks) N{N} and A{A} must not be next to one another,

(iii) (3 marks) between the two T{T}s there must be at least 8 other letters

(iv) (3 marks) consonants (P,R,M,T,N{P,R,M,T,N}) and vowels (E,U,A,I,O{E,U,A,I,O}) must alternate.

(b) Each letter in PERMUTATION{PERMUTATION} is printed on individual cards such that cards containing the same letter are considered identical. A "codeword" is formed by using some of these cards in a certain order.

(i) (3 marks) Find the number of possible "codewords" that can be formed with 3 cards.

(ii) (3 marks) Find the number of possible "codewords" that can be formed with 4 cards.

This question is inspired by the 2009 A Levels H2 Mathematics Paper 2 Question 8.
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