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# I saw these on another forum-I think business week. 1. There

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Manager
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I saw these on another forum-I think business week. 1. There [#permalink]  16 Sep 2003, 08:26
I saw these on another forum-I think business week.

1. There are 5 English, 3 Spanish and 2 Portuguese books on a shelf. If 2 books are selected without replacement what is the probability that they will be of different languages.

2. What is the greatest prime number 2^100 - 2^96 is evenly divisible by?
CEO
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Re: Can't figure these out [#permalink]  16 Sep 2003, 08:41
1. There are 5 English, 3 Spanish and 2 Portuguese books on a shelf. If 2 books are selected without replacement what is the probability that they will be of different languages.

Prob that two selected are same
5/10*4/9 + 3/10*2/9 + 2/10 * 1/9 = 14/45

Probability that they are different = 1- 14/45 = 31/45

2. What is the greatest prime number 2^100 - 2^96 is evenly divisible by

2^96(2^4 -1 ) = 2^96 *15 = 2^96 * 3 * 5

So the greatest Prime number that can divide the expression is 5

Thanks
Praetorian

Last edited by Praetorian on 16 Sep 2003, 08:46, edited 1 time in total.
Manager
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thanks, I was stuck using combo on 1.
Manager
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Same reasoning as praetorian123's.
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