<ol class="abc-list"><li><div class="list-item-paragraph">Find the number of ways in which the letters of the word NATIONAL can be arranged if</div><ol class="i-list"><li><div class="list-item-paragraph">there are no restrictions,</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">not all the identical letters are next to each other,</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">the vowels must not be next to one another.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">no two adjacent letters are the same.</div><p style="text-align: right;">[3]</p></li></ol></li><li><div class="list-item-paragraph">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.</div><div class="list-item-paragraph">Find the number of ways the group can be chosen if it includes</div><ol class="i-list"><li><div class="list-item-paragraph">exactly three trumpet players, two horn players, two trombone players and two saxophone players,</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">at least three players from each of the trumpet and saxophone sections.</div><p style="text-align: right;">[3]</p></li></ol></li></ol>

Find the number of ways in which the letters of the word NATIONAL can be arranged if

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.

2012 NJC P2 Q7 [Modified]

2012 NJC P2 Q7 [Modified]

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