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

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Intern
Joined: 01 Sep 2010
Posts: 20
Annie has 100 cards numbered 1 through 100. If she deals  [#permalink]

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Updated on: 09 Jul 2013, 08:46
5
19
00:00

Difficulty:

75% (hard)

Question Stats:

53% (02:18) correct 47% (02:30) wrong based on 188 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?

A. 95!/100!

B. 96!/100!

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

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

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

Originally posted by eladshush on 04 Oct 2010, 06:48.
Last edited by Bunuel on 09 Jul 2013, 08:46, edited 1 time in total.
RENAMED THE TOPIC.
Math Expert
Joined: 02 Sep 2009
Posts: 56257
Re: Probability for consecutive numbers  [#permalink]

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04 Oct 2010, 06:59
4
5
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, $$P=\frac{favorable \ outcomes}{total \ # \ of \ outcomes}=\frac{96}{C^5_{100}}=\frac{5!*96!}{100!}$$.

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##### General Discussion
Intern
Joined: 04 Oct 2010
Posts: 1
Re: Probability for consecutive numbers  [#permalink]

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04 Oct 2010, 07:05
Nice question! THanks for the explanation.
Manager
Joined: 07 Oct 2006
Posts: 58
Location: India
Re: Probability for consecutive numbers  [#permalink]

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04 Oct 2010, 08:23
excellent explanation... bunuel, you make tough questions seems so simple.... Awesome...
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Joined: 20 Apr 2010
Posts: 174
Schools: ISB, HEC, Said
Re: Probability for consecutive numbers  [#permalink]

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06 Oct 2010, 02:18
Thanks Bunuel great explaination
Manager
Joined: 02 Sep 2018
Posts: 117
Re: Annie has 100 cards numbered 1 through 100. If she deals  [#permalink]

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06 Jan 2019, 03:11
The correct explaination is there are 100 numbers.
Within them 95 numbers are not in serial and only 5 in serial.
so now total possible permutaion is 95 + 1=96
so the answer is 96!*5!/100!
Re: Annie has 100 cards numbered 1 through 100. If she deals   [#permalink] 06 Jan 2019, 03:11
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# Annie has 100 cards numbered 1 through 100. If she deals

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