maths nCr and nPr 3

[匿名]

2010-08-11 7:21 am

please help me. I need steps. (solution at the bottom) thank you. 5 marks

3. Peter plans to deliver 12 packages to 12 different spots.

(a) 3 packages will be delivered to 3 spots in the same district, so they will be delivered successively. How many delivery sequences does he have now?

(b) Apart from the 3 packages mentioned in (a), there are 4 packages to be delivered to 4 spots in another district successively. How many delivery sequences does he have now?

4. Given 2 x 37 x 47 x 67 x 97 = 22 603 522. How many positive even factors of 22 603 522 are there? Hint: Is 2 x 37 a positive even factor? Is 2 x 47 x 67 a positive even factor?

Solutions:
3. (a) 21 772 800
(b) 725 760
4. 16

回答 (1)

用戶2053

2010-08-11 10:06 am

✔ 最佳答案

3a)Since 3 packages will be delivered to 3 spots in the same district ,there are 12 - 3 + 1 = 10 difference district. (3P3)(10P10) = 21 772 800 delivery sequences.b)There are 12 - 3 + 1 - 4 + 1 = 7 difference district.(3P3)(4P4)(7P7) = 725 760 delivery sequences.
4) 2 x 37 x 47 x 67 x 97 = 22 603 522.For 2 , 37 , 47 , 67 , 97 ,A even factor must be including a factor '2' , must be included , (1 possible)may be including 37 , 47 , 67 , 97 as a factor , include or not include ,
(2 possible)1 * 2 * 2 * 2 * 2 = 16 positive even factor

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