F.5 Maths questions!!(Pnr,Cnr)

2014-04-24 9:06 am

1) My phone number is "9XXXXXXX" , find the combination that all of the 8 digit are different.

2) If John randomly draw card from 52 cards(A to K) without replacement, once "J" appeared, the game will be finished. How many times(at most) he need to draw to finish the game?

3) An Elimination Series for 32 player's tennis match has launched. Once the player loses in any match(there is no draw game), he will be dumped out. How many matches he need to take for producing the final champion?

回答 (1)

用戶26240

2014-04-24 12:50 pm

✔ 最佳答案

1.
The 1st digit is "9". (1)
Out of the rest 9 digits, arrange 7 different digits to form the phone number.(9P7)

The no. of combinations
= 1 x 9P7
= 9!/2!
= 181440

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2.
There are 4 cards which are "J", and 48 cards which are not"J".

In the worse case, John at first draw all the 48 cards which are not"J", and 4 cards of "J" are left.
If so, the 49th card must be "J".

No. of cards at most he needs to draw to finish the game = 49

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3.
No. of matches in the 1st round = 32 ÷ 2 = 16
No. of matches in the 2nd round = 16 ÷ 2 = 8
No. of matches in the 3nd round = 8 ÷ 2 = 4
No. of matches in the 4nd round = 4 ÷ 2 = 2
No. of matches in the 5nd round (final) = 2 ÷ 2 = 1

Total no. of matches
= 16 + 8 + 4 + 2 + 1
= 31

Alternative method :
In each match, a player is dumped out.
Apart from the final champion, all other 31 players are dumped out.
Total no. of matches = No. of players dumped out = 31

參考: 土扁

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