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Dan
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If 16 oranges are distributed among 4 children such that Updated on: 06 Jun 2005, 23:44
Originally posted by Dan on 06 Jun 2005, 06:27.
Last edited by Dan on 06 Jun 2005, 23:44, edited 1 time in total.
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If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is?

a. 30
b. 210
c. 15
d. 35



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If 16 oranges are distributed among 4 children such that Updated on: 07 Jun 2005, 00:03
Originally posted by sparky on 06 Jun 2005, 14:21.
Last edited by sparky on 07 Jun 2005, 00:03, edited 1 time in total.
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Dan
If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is?
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4 4 4 4
3 4 4 5
3 3 5 5
3 3 4 6
3 3 3 7

1+ 2*4c2 + 4c2 + 2*4c2 + 4 = 1+ 12 + 6 + 12 + 4 = 35
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If 16 oranges are distributed among 4 children such that 06 Jun 2005, 23:45
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I have added answer choices just maybe to make things easier!
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If 16 oranges are distributed among 4 children such that 07 Jun 2005, 01:46
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Dan
If 16 oranges are distributed among 4 children such that each gets at least 3 oranges, the number of ways of distributing them is?

a. 30
b. 210
c. 15
d. 35
Show more


Since each child gets at least 3...12 oranges can be removed...there are four remaining
these can be distributed as follows:
a)1 1 1 1
b)4 0 0 0
c)2 2 0 0
d)2 1 1 0
e)3 1 0 0

Number of ways to do a = 1

Number of ways to do b = 4

Number of ways to do c = 4C2 = 6

Number of ways to do d = 2*4C2 = 12

Number of ways to do e = 4*3=12

1+4+6+12+12 = 35
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If 16 oranges are distributed among 4 children such that 07 Jun 2005, 10:11
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OA 35.

not getting 2*4C2 and 4C2?

Also, the using of the formula (n+r-1) C(r-1) ??
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If 16 oranges are distributed among 4 children such that 08 Jun 2005, 02:58
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Dan
OA 35.

not getting 2*4C2 and 4C2?

Also, the using of the formula (n+r-1) C(r-1) ??
Show more


The no. of ways to distribute n items among r ppl where each gets zero or more items is (n+r-1) C(r-1).

In our current case the no. of ways is really dependant on the way we distribute the remaining of ( 4*3 ) oranges , which is 4.

We have to distribute 4 oragnes to 4 ppl , with each gets zero or more oranges.

here n = r = 4
the formula reduces to (4 + 4 -1 ) C ( 4-1 ) = 7c3 = 35.

HMTG.



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Hi there,
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