Question

This is a Combinatorics question.

Find a generating function for a sub r, the number of ways:

(1) To distribute ridentical objects into seven distinct boxes with an odd numbet of objects not exceeding nine in the first three boxes and between four and ten in the other boxes.

Answer 1

If there are two jobs such that one of them can be completed in ‘m’ ways, and another one in ‘n’ ways then the two jobs in succession can be done in ‘m X n’ ways."

Example :- In her class of 10 girls and 8 boys, the teacher has to select 1 girl AND 1 boy. In how many ways can she make her selection?
Here the teacher has to choose the pair of a girl AND a boy

For selecting a boy she has 8 options/ways AND that for a girl 10 options/ways
For 1st boy ------- any one of the 10 girls ----------- 10 ways
For 2nd boy ------- any one of the 10 girls ----------- 10 ways
For 3rd boy ------- any one of the 10 girls ----------- 10 ways
-------------
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For 8th boy ------- any one of the 10 girls ----------- 10 ways
Total number of ways 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 = 8b0 ways OR 10 X 8 = 80 ways.

Remark :- The above principle can be extended for any finite number of jobs.


Fundamental Principle of Addition