+107 A band has a portfolio of 15 songs. 5 are acoustic. For a concert the band will play 10distint songs, 4 will be acoustic. The 4 acoustic will be played consecutively during the 2nd half, but withou ending in anacoustic song. How many different sequences of the songs are possible?
+6251 looking at the 2nd half of the show firstthe songs will be AAAA!Athere are 4!=24 ways to arrange the 4 acoustic songs, and10 ways to select the !A song at the endthis is then 240 ways to arrange the 2nd half of the showthe first half of the show is then 5 non-acoustic songs chosen from 9since we care about order there are (95)5!=15120 arrangements for the first halfso in total we have240×15120=3628800 possible concert arrangements
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