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 – 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.
CAT-holics 
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 🙂
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 – 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 🙂
regards
J
Thanks a lot! 😀