2012 NJC P2 Q7 [Modified]
(a)
Find the number of ways in which the letters of the word NATIONAL can be arranged if
(i) there are no restrictions,
[1]
(ii) not all the identical letters are next to each other,
[2]
(iii) the vowels must not be next to one another.
[2]
(iv) no two adjacent letters are the same.
[3]
(b)
The Rational Junior College Symphonic Band comprises four trumpet players, four horn players, three trombone players and four saxophone players. A mini stage band of nine players are to be chosen from these sections to perform for a segment of their annual concert.
Find the number of ways the group can be chosen if it includes
(i) exactly three trumpet players, two horn players, two trombone players and two saxophone players,
[2]
(ii) at least three players from each of the trumpet and saxophone sections.
[3]
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