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A shop sells 5 different types of sweets. In how many different ways

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Bunuel
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A shop sells 5 different types of sweets. In how many different ways [#permalink] New post   25 Jun 2021, 08:15
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41% (01:40) correct 59% (02:34) wrong based on 70 sessions
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A shop sells 5 different types of sweets. In how many different ways a total of 8 sweets can be purchased?

(A) 125
(B) 495
(C) 795
(D) 840
(E) 930
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B
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chetan2u
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Re: A shop sells 5 different types of sweets. In how many different ways [#permalink] New post   27 Jun 2021, 07:52
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Bunuel wrote:
A shop sells 5 different types of sweets. In how many different ways a total of 8 sweets can be purchased?

(A) 125
(B) 495
(C) 795
(D) 840
(E) 930



Quickest way : Use partition method and the formula involved.
The equation can be written as \(a+b+c+d+e=8\), and we have find non negative solutions for the same
If there are 4 partitions, the answer would be (8+4)C4=\(\frac{12!}{8!/4!}=\frac{12*11*10*9}{4*3*2}=495\)

You can also calculate each type


B
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Re: A shop sells 5 different types of sweets. In how many different ways [#permalink] New post   27 Jun 2021, 08:14
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Bunuel wrote:
A shop sells 5 different types of sweets. In how many different ways a total of 8 sweets can be purchased?

(A) 125
(B) 495
(C) 795
(D) 840
(E) 930



total possible ways
n+r-1 cr-1

8+5-1 c 5-1
12c4 = 495
option B
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Re: A shop sells 5 different types of sweets. In how many different ways [#permalink] New post   10 Oct 2022, 05:04
chetan2u wrote:
Bunuel wrote:
A shop sells 5 different types of sweets. In how many different ways a total of 8 sweets can be purchased?

(A) 125
(B) 495
(C) 795
(D) 840
(E) 930



Quickest way : Use partition method and the formula involved.
The equation can be written as \(a+b+c+d+e=8\), and we have find non negative solutions for the same
If there are 4 partitions, the answer would be (8+4)C4=\(\frac{12!}{8!/4!}=\frac{12*11*10*9}{4*3*2}=495\)

You can also calculate each type


B



You distributed 8 boxes of sweets among 5 sweets. That's a great approach.
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Re: A shop sells 5 different types of sweets. In how many different ways [#permalink]
10 Oct 2022, 05:04
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