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# Paul and Allen are choosing ties out of a selection of three distinct

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Math Expert
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Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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07 Dec 2018, 03:23
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:24) correct 37% (01:22) wrong based on 89 sessions

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Paul and Allen are choosing ties out of a selection of three distinct red ties, five distinct green ties, and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could they wear ties of the same color?

A. 6
B. 20
C. 30
D. 36
E. 56

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Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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07 Dec 2018, 05:14
1
Bunuel wrote:
Paul and Allen are choosing ties out of a selection of three distinct red ties, five distinct green ties, and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could they wear ties of the same color?

A. 6
B. 20
C. 30
D. 36
E. 56

red 3*2
green 5*4
blue 6*5

total 6+20+30= 56 IMO E
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Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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07 Dec 2018, 11:56
Given 3 Red , 5 Green , 6 Blue .
If P chooses Red , A should also choose Red => 3*2 ways
green => 5*4 ways
Blue => 6*5 ways
Total = 6+20+30 = 56 ways - Option E
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Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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Updated on: 29 Dec 2018, 06:44
$$3P2 = 6$$
$$5P2 = 20$$
$$6P3 = 30$$

= 56 / E

Originally posted by mskx on 28 Dec 2018, 06:08.
Last edited by mskx on 29 Dec 2018, 06:44, edited 1 time in total.
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Posts: 516
Location: India
Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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28 Dec 2018, 07:41
Bunuel wrote:
Paul and Allen are choosing ties out of a selection of three distinct red ties, five distinct green ties, and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could they wear ties of the same color?

A. 6
B. 20
C. 30
D. 36
E. 56

Given: 3 distinct Red ties, 5 distinct Green ties, and 6 distinct Blue ties

Required : # of ways could Paul and Allen wear ties of same color

The # of ways = (# of ways both wear Red tie) or (# of ways both wear Green tie) or (# of ways both wear Blue tie)

= (3*2) + (5*4) + (6*5) = 6 + 20 + 30 = 56 ways

Thanks,
GyM
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Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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29 Dec 2018, 06:07
mskx wrote:
$$3P2 = 3$$
$$5P2 = 20$$
$$6P3 = 30$$

= 56 / E

I guess there is a little typo

should be

$$3P2 = 6$$
$$5P2 = 20$$
$$6P2 = 30$$
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Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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06 Jan 2019, 04:02
Archit3110 wrote:
Bunuel wrote:
Paul and Allen are choosing ties out of a selection of three distinct red ties, five distinct green ties, and six distinct blue ties. If Paul and Allen each wear one tie, how many different ways could they wear ties of the same color?

A. 6
B. 20
C. 30
D. 36
E. 56

red 3*2
green 5*4
blue 6*5

total 6+20+30= 56 IMO E

Could you please explain why is this a permutation problem ?
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Joined: 18 Apr 2018
Posts: 93
Re: Paul and Allen are choosing ties out of a selection of three distinct  [#permalink]

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11 Jan 2019, 04:36
I am also not quite sure as to why order matters here or whether it makes any difference for paul or Allen to pick a tie if the colors are the same. Please help my understanding... Bunuel

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Re: Paul and Allen are choosing ties out of a selection of three distinct   [#permalink] 11 Jan 2019, 04:36
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