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15. There are 5 different marshmallows, 7 different fruit drops and 12 different pieces of chocolate in a candy box. If 4 candies are picked and some of them are of the different types, find number of combinations.
16. There are 16 empty boxes. First, fill in any 4 boxes with black colour. Now we have 8 different colour pens without black colour. To fill in any 5 remaining boxes in the pattern obtained previously with different colours, how many different patterns can be formed?
17. There are 80 people in a choir. The choirmaster plans to choose 8 people and arrange them in a row for a performance. It is given that Timothy and Susan are chosen as the performers. The choirmaster chooses another 6 people at random. If Timothy cannot be arranged at the leftmost of the row and Susan cannot be arranged at the rightmost, find number of permutations.
Solutions:
15. 10 091
16. 9 686 476 800
17. 7.95 x 10^12
maths nCr and nPr 10
2010-08-11 7:04 pm
回答 (2)
2010-08-12 1:53 am
✔ 最佳答案
15.(5+7+12)C4 - 5C4 - 7C4 - 12C4= 10 09116.Fill in any 4 boxes with black colour of 16 empty boxes :16C4 = 1820 waysAny 5 remaining boxes out of 12 empty boxes :12C5 = 792 cases5 boxes with 5 different colour out of 8 :8P5 = 6720 ways ,Answer : 1820 x 792 x 6720 = 9 686 476 800
17)All permutations - All Timothy at the leftmost permutations - All Susan at the rightmost permutations + Timothy at the leftmost and Susan at the rightmost permutations = (78C6) (8P8 - 7P7 - 7P7 + 6P6)= 7.95 x 10^12
2010-08-11 9:36 pm
收錄日期: 2021-04-19 23:00:45
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