Geoff is setting up an aquarium and must choose 4 of 6 different fish

Question

Geoff is setting up an aquarium and must choose 4 of 6 different fish and 2 of 3 different plants. How many different combinations of fish and plants can Geoff choose?

A. 8
B. 12
C. 18
D. 45
E. 90

Nikhil · Answer

Number of ways of selecting 4 fish from 6 fish are  6c_4  =  \frac{6!}{4!2!}  = 15

Number of ways of selecting 2 plants from 3 plants are  3c_2  =  \frac{3!}{2!}  = 3

Number of different combinations of fish and plants Geoff can choose = 15 * 3 = 45

Hence  option D

PKN · Answer

No of combinations of fish and plant = no of ways of choosing 4 dishes out of 6* no of ways of choosing 2 plants out of 3=6C4*3C2=5*3=15

Ans. (D)

Posted from my mobile device

EgmatQuantExpert · Answer

Solution

Given:  
 • Geoff is setting up an aquarium and must choose 4 of 6 different fish and 2 of 3 different plants

To find:  
 • In how many different combinations Geoff can choose fish and plants

Approach and Working:   
Geoff needs to choose 4 out of 6 different fish
 • Number of ways he can choose fish =  ^6C_4  = 15

Geoff needs to choose 2 out of 3 different plants
 • Number of ways he can choose plant =  ^3C_2  = 3

Therefore, total number of ways Geoff can make the choices = 15 * 3 = 45

Hence, the correct answer is option D.

Answer: D

sudarshan22 · Answer

+1 for   D  .

Number of ways to choose fish = 6C4
Number of ways to choose plant = 3C2

Total number of ways to make the choices = 6C4*3C2 = 15 * 3 = 45

Hence,   D  .

LordStark · Answer

this is an AND question 
4 fish selected out of 6, (sequence of selection doesn't matter ), total combinations = \frac{6!}{4!*2!}

2 plants selected out of 3, (sequence of selection doesn't matter ), total combinations = \frac{3!}{1!*2!}

= \frac{6!}{4!*2!}  *  \frac{3!}{1!*2!}  = 45

ScottTargetTestPrep · Answer

The number of fish can be selected in 6C4 ways:

6! / (2! x (6 - 2)!) = 6!/(2! x 4!) = (6 x 5 x 4 x 3)/(4 x 3 x 2) = 15 ways

The number of plants can be selected in 3C2 = 3 ways.

So the total number of arrangements is 15 x 3 = 45.

Answer: D

StudiosTom · Answer

I did the first 2 portions and found 15 and 3.could not as decide whether I should use multiply or add.How do we decide?
@chetan2u,@VeritasPrepKarishma,@ScottTargetTestPrep

bumpbot · Answer

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Geoff is setting up an aquarium and must choose 4 of 6 different fish

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