Subjects combinatorics

Osis Photo

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Osis Photo


1. Given 11 people lined up for a photo. 2. The ketua (chairperson) must be in the middle position (which is position 6). 3. The sekretaris (secretary) and bendahara (treasurer) must be on either side of the ketua. 4. Positions: sekretaris in 5 or 7, bendahara in the remaining position next to ketua. 5. There are 2 possible ways to arrange sekretaris and bendahara around ketua: sekretaris left & bendahara right, or vice versa. 6. After placing these three, 8 people remain to be arranged in 8 remaining positions. 7. Number of ways to arrange the remaining 8 people is $8!$. 8. Total possible arrangements = $2 \times 8!$. Thus, the number of possible photo arrangements is $2 \times 8!$.