7 thoughts on “Identical objects, distinct groups”

Sir,

Firstly, thank you for this blog ! It is of immense help to Non-math background students.

For the Q5.if the fish were all distinct then the number of combinations would have been 5^12, right? (Sending n distinct objects to r distinct places).

Hi J,
I have a doubt, I recently came across this question in a mock exam, A young princess was walking in a garden full of flowers of five different varieties â€“ Jasmine’s, Tulips, Daffodils, Lilies and Roses. In how many ways can she pick 12 flowers for her grandmother?

I tried to use the FPC and ended up with 5 to the power 12 and the answer, was wrong and it used the partitions logic in the solution, could explain why?

Because all flowers of a given type are identical. And the order of picking flowers is not relevant. If you are doing 5^12 basically you are saying that the first being a rose and the second a tulip is different from the first being a tulip and the second a rose.

Sir,

Firstly, thank you for this blog ! It is of immense help to Non-math background students.

For the Q5.if the fish were all distinct then the number of combinations would have been 5^12, right? (Sending n distinct objects to r distinct places).

Please correct me if wrong.

Thanks.

Yes that’s quite correct ðŸ™‚

regards

J

Hi J,

I have a doubt, I recently came across this question in a mock exam, A young princess was walking in a garden full of flowers of five different varieties â€“ Jasmine’s, Tulips, Daffodils, Lilies and Roses. In how many ways can she pick 12 flowers for her grandmother?

I tried to use the FPC and ended up with 5 to the power 12 and the answer, was wrong and it used the partitions logic in the solution, could explain why?

Because all flowers of a given type are identical. And the order of picking flowers is not relevant. If you are doing 5^12 basically you are saying that the first being a rose and the second a tulip is different from the first being a tulip and the second a rose.

regards

J

Hello Sir,

Is the answer 16C4 then?

That would seem a reasonable answer, yes ðŸ™‚

regards

J

Thanks a lot! ðŸ˜€