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

Question

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

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

Archit3110 · Answer

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

total 6+20+30= 56 IMO E

baru · Answer

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

mskx · Answer

3P2 = 6 
 5P2 = 20 
 6P3 = 30

= 56 / E

GyMrAT · Answer

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

Answer E.

Thanks,
GyM

gzuz · Answer

I guess there is a little typo

should be

3P2 = 6 
 5P2 = 20 
 6P2 = 30

kanakdaga · Answer

Could you please explain why is this a permutation problem ?

Kem12 · Answer

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

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