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Jeremy needs to choose three flowers for his mother from a group of 10

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Jeremy needs to choose three flowers for his mother from a group of 10 [#permalink]

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New post 05 Jan 2016, 09:33
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Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?

A) 30:1
B) 10:1
C) 5:1
D) 3:2
E) 1:5
[Reveal] Spoiler: OA

Last edited by ENGRTOMBA2018 on 05 Jan 2016, 09:39, edited 1 time in total.
Added the OA
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Re: Jeremy needs to choose three flowers for his mother from a group of 10 [#permalink]

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New post 05 Jan 2016, 09:42
joemcent wrote:
Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?

A) 30:1
B) 10:1
C) 5:1
D) 3:2
E) 1:5


Make sure to add the official answer (OA). I have edited your question to add the OA.

As for the question, you are given 10 roses out of which 6 are red and 4 are white.

Ways of selecting 3 red roses only out of 6 available = 6C3 = 6!/(3!*3!)

Similarly, Ways of selecting 3 white roses only out of 4 available = 4C3 = 4!/(3!*1!)

Thus the ratio = 6C3/4C3 = 5:1

C is the correct answer.
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Re: Jeremy needs to choose three flowers for his mother from a group of 10 [#permalink]

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New post 26 Mar 2017, 01:47
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Re: Jeremy needs to choose three flowers for his mother from a group of 10 [#permalink]

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New post 26 Mar 2017, 05:51
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joemcent wrote:
Jeremy needs to choose three flowers for his mother from a group of 10 roses, six of which are red and four of which are white. What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?

A) 30:1
B) 10:1
C) 5:1
D) 3:2
E) 1:5


It's implied that the 6 red roses are not identical, and the 4 which roses are not identical.

In how many ways can we select 3 red roses from 6 red roses?
Since the order in which we select the 3 red roses does not matter, we can use combinations.
We can select 3 red roses from 6 red roses in 6C3 ways (= 20 ways)

Likewise, we can use combinations to count the number of ways to select 3 white roses.
We can select 3 white roses from 4 white roses in 4C3 ways (= 4 ways)

What is the ratio of the number of ways in which he can select only red roses to the number of ways in which he can select only white roses?
= 20 : 4
= 5 : 1

Answer:
[Reveal] Spoiler:
C


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Re: Jeremy needs to choose three flowers for his mother from a group of 10   [#permalink] 26 Mar 2017, 05:51
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