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Quiz of the Month (October 2008)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

  1.  720
  2.  120
  3.  1,000
  4.  220

Notes. 1. Prize no.1 can be awarded in 10 ways. Then prize no.2 can be awarded in 9 ways. Then prize no.3 can be awarded in 8 ways. 10 * 9 * 8 = 720 2. The prizes in Q.1 may be re-arranged in 6 ways. So the 720 arrangements fall into groups of 6. The arrangments within each group become identical in Q.2. 720 / 6 = 120 3. 10 * 10 * 10 = 1,000 4. No. of ways if prizewinners all different = 120 No. of ways if one prizewinner gets two = 10 * 9 = 90 No. of ways if one prizewinner gets three = 10 120 + 90 + 10 = 220

THIS MONTH'S QUIZ

1. A bag contains nine blue balls, six red ones, three yellow ones, and one green one. How many balls must be taken out, without looking, to ensure that you have (a) at least two of the same colour, (b) at least five of the same colour?

2. If the larger circle has twice the diameter of the smaller circle, through how many degrees will the small circle turn in rolling, without slipping, once around the inside of the large one?

3. If the larger circle has 11/2 times the diameter of the smaller circle, through how many degrees will the small circle turn in rolling, without slipping, once around the inside of the large one?

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© Hector C. Parr (2008)

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