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# John has 7 bananas and 3 kiwis. In how many ways can John

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Manager
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John has 7 bananas and 3 kiwis. In how many ways can John [#permalink]

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06 Jan 2005, 12:41
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John has 7 bananas and 3 kiwis. In how many ways can John divide the 10 fruit between two parcels, if there has to be an equal total number of fruit in either parcel and so that there is at least one kiwi in each parcel.

A. 21
B. 35
C. 60
D. 105
E. 120
Manager
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06 Jan 2005, 13:01
kdhong wrote:
John has 7 bananas and 3 kiwis. In how many ways can John divide the 10 fruit between two parcels, if there has to be an equal total number of fruit in either parcel and so that there is at least one kiwi in each parcel.

A. 21
B. 35
C. 60
D. 105
E. 120

For each parcel to have at least one kiwi, one of the two parcel has to have either 1 or 2 kiwis. Let's look at the possibilities of combinations:

Combo 1:

1 kiwi + 4 bananas for parcel #1; 2 kiwis + 3 bananas for parcel #2
3C1 x 7C4 = 3 x 35 = 105 ways to arrange

Combo 2:

2 kiwis + 3 bananas for parcel #1; 1 kiwi + 4 bananas for parcel #2
3C2 x 7C3 = 3 x 35 = 105 ways to arrange

Since combo 1 is equal to combo 2, so there are only 105 ways to arrange the fruits, and the answer is D.
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06 Jan 2005, 13:13
"D". 105

As there is a no distinction between 2 parcels, there is 1 way to choose a parcel, once a parcel is chosen we can put the required fruits on that and rest of the fruits can be put in only 1 way for the other parcel.

So choosing 4 bananas and 1 kiwi.

1x(7C4x3C1) = 105.
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