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## Quiz of the Month (March 2004)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

```    1.  15
2.  105
3.  654729075```

Notes

(Notice that the question asks for the number of ways in which all the players can be paired off, not the number of ways of selecting one pair.)

1. A's partner can be chosen in 5 ways.
Then remaining 4 people can be paired in 3 ways (as explained in the question).
So total no. of pairings = 5 * 3

2. A's partner can be chosen in 7 ways.
Then remaining 6 people can be paired in 5 * 3 ways.
So total no. of pairings = 7 * 5 * 3

3. And so on ......
So total no. of pairings = 19 * 17 * 15 * 13 * 11 * 9 * 7 * 5 * 3

#### THIS MONTH'S QUIZ

Two points are marked, randomly and independently, on a metre ruler, and the ruler is broken at these points into three pieces.

1. What is the probability that the left hand piece measures less than 50 cm?

2. What is the probability that the longest piece measures less than 50 cm?

3. What is the probability that the middle piece is the shortest of the three?

***

(c) Hector C. Parr (2004)

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