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Annie has 100 cards numbered 1 through 100. If she deals [#permalink]

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Updated on: 09 Jul 2013, 08:46

5

10

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

55% (01:38) correct 45% (01:51) wrong based on 133 sessions

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Annie has 100 cards numbered 1 through 100. If she deals five cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?

Re: Probability for consecutive numbers [#permalink]

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04 Oct 2010, 06:59

2

5

eladshush wrote:

Annie has 100 cards numbered 1 through 100. If she deals five cards to Alex, without replacing any of them, what is the probability that Alex will get five consecutive numbers?

A. 95!/100!

B. 96!/100!

C. (95! X 5!)/100!

D. (96! X 5!)/100!

E. (97! X 4!)/100!

I guess it's not necessary Alex to get 5 consecutive cards in ascending order, to have 5 consecutive at the end is good enough.

There are 96 consecutive numbers in 100: {1, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, ..., {96, 97, 98, 99, 100}; Total ways to pick 5 cards out of 100 is \(C^5_{100}\);

So, \(P=\frac{favorable \ outcomes}{total \ # \ of \ outcomes}=\frac{96}{C^5_{100}}=\frac{5!*96!}{100!}\).

Re: Annie has 100 cards numbered 1 through 100. If she deals [#permalink]

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16 Oct 2017, 21:12

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