Answer:
1. This is a permutation problem number of ways 12 people can be arranged in row
12!
12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
132 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
1,320 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
11,880 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
95,040 × 7 × 6 × 5 × 4 × 3 × 2 × 1
665,280 × 6 × 5 × 4 × 3 × 2 × 1
3,991,680 × 5 × 4 × 3 × 2 × 1
19,958,400 × 4 × 3 × 2 × 1
79,833,600 × 3 × 2 × 1
239,500,800 × 2 × 1
479,001,600 × 1
2. This is a permutation problem of ways 15 people can be line themselves in flag ceremony
15!
15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
210 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
2,730 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
32,760 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
360,360 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
3,603,600 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
32,432,400 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
259,459,200 × 7 × 6 × 5 × 4 × 3 × 2 × 1
1,816,214,400 × 6 × 5 × 4 × 3 × 2 × 1
10,897,286,400 × 5 × 4 × 3 × 2 × 1
54,486,432,000 × 4 × 3 × 2 × 1
217,945,728,000 × 3 × 2 × 1
653,837,184,000 × 2 × 1
1,307,674,368,000 × 1
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Verified answer
Answer:
1. This is a permutation problem number of ways 12 people can be arranged in row
12!
12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
132 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
1,320 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
11,880 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
95,040 × 7 × 6 × 5 × 4 × 3 × 2 × 1
665,280 × 6 × 5 × 4 × 3 × 2 × 1
3,991,680 × 5 × 4 × 3 × 2 × 1
19,958,400 × 4 × 3 × 2 × 1
79,833,600 × 3 × 2 × 1
239,500,800 × 2 × 1
479,001,600 × 1
= 479,001,600 ways
2. This is a permutation problem of ways 15 people can be line themselves in flag ceremony
15!
15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
210 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
2,730 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
32,760 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
360,360 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
3,603,600 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
32,432,400 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
259,459,200 × 7 × 6 × 5 × 4 × 3 × 2 × 1
1,816,214,400 × 6 × 5 × 4 × 3 × 2 × 1
10,897,286,400 × 5 × 4 × 3 × 2 × 1
54,486,432,000 × 4 × 3 × 2 × 1
217,945,728,000 × 3 × 2 × 1
653,837,184,000 × 2 × 1
1,307,674,368,000 × 1
= 1,307,674,368,000 ways