in how many ways can the following prizes be given away to a class of 30 students, first and second - Maths - Permutations and Combinations

Question

in how many ways can the following prizes be given away to a class
of 30 students, first and second in Mathematics, first and second
in Physics, first in Chemistry and first in English?

Mohammed Irfan Khan · Accepted Answer

Dear Student

First prize in mathematics can be given in =30 ways second prize in mathematics can be given in  =29 ways First prize in physics can be given in =30 ways second prize in physics can be given in =29 ways First prize in chemistry can be given in =30 ways similarly, first prize in English can be given in =30 ways All the 6 prizes can be given in = 30×29×30×29×30×30 ways                                                         =681,210,000 ways Hence, Total number of ways to distribute all 6 prizes =681210000
Regards

in how many ways can the following prizes be given away to a class of 30 students, first and second in Mathematics, first and second in Physics, first in Chemistry and first in English?