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Alfred, ever hungry, decides to order 4 desserts after his meal. If

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Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 24 Jul 2017, 22:48
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Alfred, ever hungry, decides to order 4 desserts after his meal. If there are 7 types of pie and 8 types of ice cream from which to choose, and Alfred will have at most two types of ice cream, how many distinct groups of desserts could he consume in his post-prandial frenzy?

A. 588
B. 868
C. 903
D. 1806
E. 2010

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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 24 Jul 2017, 23:01
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Given data: There are 7 pies and 8 ice-creams to choose from.
Since Alfred decides to go with at most 2 ice-creams, out of the total 4 deserts.
He can have 0,1 or 2 ice-cream.

If he decides to have no ice cream :
Number of ways of choosing dessert(4 pies) : \(7c4 = \frac{7*6*5}{3*2}\) = 35 ways

If he decides to have 1 ice cream :
Number of ways of choosing dessert(3 pies and 1 ice-cream) : \(7c3*8c1 = \frac{7*6*5}{3*2} * 8 = 270\) ways

If he decides to have 2 ice cream :
Number of ways of choosing dessert(2 pies and 2 ice-cream) : \(7c2*8c2 = 49 * 12 = 588\) ways

Total ways in which Alfred choose dessert - \(35 + 270 + 588 = 903\)(Option C)
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Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post Updated on: 25 Jul 2017, 03:05
2 ice-creams + 2 pies = 8c2 * 7c2 = 28 * 21 = 588
1 ice-cream + 3 pies = 8c1 * 7c3 = 8 * 35 = 280
0 ice-cream + 4 pies = 7c4 = 35

No. of desserts = 903. Ans - C.
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Originally posted by TimeTraveller on 24 Jul 2017, 23:58.
Last edited by TimeTraveller on 25 Jul 2017, 03:05, edited 1 time in total.
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 25 Jul 2017, 00:43
Bunuel wrote:
Alfred, ever hungry, decides to order 4 desserts after his meal. If there are 7 types of pie and 8 types of ice cream from which to choose, and Alfred will have at most two types of ice cream, how many distinct groups of desserts could he consume in his post-prandial frenzy?

A. 588
B. 868
C. 903
D. 1806
E. 2010


2 ice cream 2 pie = 7C2 * 8C2 = 21*28 = 588
1 icecream 3 pie = 7C3 * 8C1 = 35 * 8 = 280
0 ice cream and 4 pie = 7C4 = 35

903
C
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 25 Jul 2017, 10:48
A very basic doubt here...why do we not consider that he orders 4 quantities of a single type of pie or ice-cream?
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 25 Jul 2017, 18:23
Novice90 wrote:
A very basic doubt here...why do we not consider that he orders 4 quantities of a single type of pie or ice-cream?


Because the question says "Alfred will have at most two types of ice cream".
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 25 Jul 2017, 20:07
TimeTraveller wrote:
Novice90 wrote:
A very basic doubt here...why do we not consider that he orders 4 quantities of a single type of pie or ice-cream?


Because the question says "Alfred will have at most two types of ice cream".

Ok. But can Alfred order 4 quantities of 1 type of ice cream or he can order total 4 quantities of 2 types of ice creams?

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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 26 Jul 2017, 22:11
Bunuel wrote:
Alfred, ever hungry, decides to order 4 desserts after his meal. If there are 7 types of pie and 8 types of ice cream from which to choose, and Alfred will have at most two types of ice cream, how many distinct groups of desserts could he consume in his post-prandial frenzy?

A. 588
B. 868
C. 903
D. 1806
E. 2010


Total Number of desserts should be 4. Condition -> At-most 2 Ice-creams
No Ice-cream + 4 Pies = 7C4 = 35
One Ice-Cream + 3 Pies = 8C1*7C3 = 280
Two Ice-Creams + 2 Pies = 8C2*7C2 = 588

Hence total number of possibilities = 35+280+588 = 903
Answer : C
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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New post 27 Jul 2017, 01:42
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Bunuel wrote:
Alfred, ever hungry, decides to order 4 desserts after his meal. If there are 7 types of pie and 8 types of ice cream from which to choose, and Alfred will have at most two types of ice cream, how many distinct groups of desserts could he consume in his post-prandial frenzy?

A. 588
B. 868
C. 903
D. 1806
E. 2010


Alfred is going to order 4 desserts.
There are 7 types of pie
and 8 types of ice cream

Also at most 2 ice creams can be ordered

Case 1 : 4 pie, no icecream
7C4 *1 = 35

Case 2 : 3 pie, 1 ice cream
7C3 * 8C1 = 7*6*5/3/2/1 * 8 = 35 *8 = 280

Case 3 : 2 pie, 2 ice cream
7C2 * 8C2 = 7*6/2 * 8*7/2 = 21*28 = 588

distinct groups of desserts = 35 + 280 + 588 = 903

Answer C
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Re: Alfred, ever hungry, decides to order 4 desserts after his meal. If  [#permalink]

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