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Contestants at a baking contest must use between 5 and 8 of

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Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 30 Dec 2017, 13:21
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Question Stats:

80% (01:03) correct 20% (01:13) wrong based on 15 sessions
Contestants at a baking contest must use between 5 and 8 of 10 possible ingredients.

Quantity A
Quantity B
The number of ingredients that must be used to get the smallest possible number of different combinations
The number of ingredients that must be used to get the largest possible number of different combinations Quantity A is greater.


A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 12
Page: 561
[Reveal] Spoiler: OA

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Re: Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 06 Jan 2018, 04:41
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Ans A.

To get smaller combinations, 8 out of 10 ingredients need to be used.

nCr for 8 ingredients = 45 combinations (Quantity A = 8)
nCr for 5 ingredients = 252 combination (Quantity B = 5)
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Re: Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 08 Jan 2018, 16:15
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Explanation

You are forming groups where order doesn’t matter, so use the combination formula.

If you use 5 ingredients, then there are: \(\frac{10}{5}\times\frac{9}{4}\times\frac{8}{3}\times\frac{7}{2}\times\frac{6}{1}=252\) different combinations.

If you use 6 ingredients there are \(\frac{10}{6}\times\frac{9}{5}\times\frac{8}{4}\times\frac{7}{3}\times\frac{6}{2}\times\frac{5}{1}=210\) combinations, if you use 7 there are \(\frac{10}{7}\times\frac{9}{6}\times\frac{8}{5}\times\frac{7}{4}\times\frac{6}{3}\times\frac{5}{2}\times\frac{4}{1}=120\), and if you use 8 there are \(\frac{10}{8}\times\frac{9}{7}\times\frac{8}{6}\times\frac{7}{5}\times\frac{6}{4}\times\frac{5}{3}\times\frac{4}{2}\times\frac{3}{1}=45\).

Thus, Quantity A is 8, and Quantity B is 5, choice A.
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Re: Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 10 Jan 2018, 01:05
Hello sandy

In questions such as between so and so value such as 5 and 8 is this always the case that the two values are inclusive?
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Re: Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 10 Jan 2018, 02:07
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In not is specified you should consider 5 and 8 included. I.E the range is not from 6 to 7 but 5 to 8.

This is a good question for practice but not the top notch. An official question must be included in the statement if they should be considered or not. To clear all the possible confusion.

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Re: Contestants at a baking contest must use between 5 and 8 of [#permalink] New post 09 Mar 2018, 03:28
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Whenever it is written from a to b, both ends must be included, but when it is written between a and b, ends are not included, its b-a-1 no of terms. Therefore, in this case its just 6 and 7.
If anyone says this then he or she is wrong. If not mentioned whether it is inclusive or not, it must be assumed inclusive.
Re: Contestants at a baking contest must use between 5 and 8 of   [#permalink] 09 Mar 2018, 03:28
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