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# A box contain a certain number of balls, marked successively from 1 to

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Re: A box contain a certain number of balls, marked successively from 1 to [#permalink]
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Turkish wrote:
A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?
1.6
2.8
3.9
4.12
5.14

hi turkish,
3 is just a number.. what actually it tells us is that we are left with one ball less ..and we have to choose two balls from it..
so we are left with n-1 ball and ans will be=(n-1)!c2=55..

(n-1)!/2!(n-3)!=55..
(n-1)(n-2)=110=11*10 so n=12.. ans 4...
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Re: A box contain a certain number of balls, marked successively from 1 to [#permalink]
1
Kudos
Turkish wrote:
A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?
1.6
2.8
3.9
4.12
5.14

Total ways of selecting 2 balls out of n balls = nC2
We're told that one balls marked as 3 cannot be selected.
So total number of balls left now = (n-1)
Hence total ways of selecting 2 balls out of (n-1) balls = (n-1)C2
Given that (n-1)C2 = 55
So, [(n-1)(n-2)]/[2 * 1] = 55
So, n^2-3n+2 = 110
So, n^2-3n-108 = 0
So, n = 12 or -9 (rejected)
Hence option 4.

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Re: A box contain a certain number of balls, marked successively from 1 to [#permalink]
Turkish wrote:
A box contain a certain number of balls, marked successively from 1 to n. If there are 55 different ways that two balls can be selected from the box such that the ball with number 3 marked on it is not selected, then what is the value of n?
1.6
2.8
3.9
4.12
5.14

we can logically deduce the value of n...
to be 55..it must be a 11 factor in the numerator. A, B, and C can be easily eliminated.
between D and E, D looks better, since 11x10/2 = 55, while 13x12/2 doesn't even have 11 as a factor..

another method...
since we need to use factorials, we can multiply 55 by 2, and 110 must be the value of n*n-1.
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Re: A box contain a certain number of balls, marked successively from 1 to [#permalink]
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Re: A box contain a certain number of balls, marked successively from 1 to [#permalink]
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