retagged by
909 views
1 votes
1 votes

What's the relationship between combination and polynomial equation? I mean, I am not able to grasp certain points here or let's say connect them into a whole:

1. Take a question where it's asked that we have to arrange 10 books : 4 of A, 3 of B, 2 of C, and 1 of D in such a way that each book of similar type remain with its own type so like AAAABBBDCCC, etc. Here we are doing 4!*4!*3!*2!*1!.

2. When we take a question of dividing 10 police officers into 3 groups: 10 -> 5,3,2. Here we use 10!/*5!*3!*2!).

3. How many solutions of $x1+x2+x3+...+xn=300$ are possible?

Doubt: What's the difference between 1 & 2? Isn't two equivalent to saying arrange 10 officers like manner of AAAAABBBCC? If we are grouping 10 distinct elements into 3 groups where each group is of same type, then what's the catch here?

Second is what's the similarity between 2 and 3? Isn't three equivalent to saying group 300 distinct element into 3 bags/groups?

I am totally confuse here and I think I cannot move ahead with my GATE preparation if I cannot clear my doubt on combinatorics which in turn would mean no way of doing probability's tricky questions.

EDIT: Here's the images of different questions. How do I differentiate between them?

retagged by

Please log in or register to answer this question.

Related questions

0 votes
0 votes
1 answer
1
atulcse asked Jan 12, 2022
312 views
How many 5-digit even numbers have all digits distinct?
0 votes
0 votes
0 answers
2
Vicky rix asked Sep 10, 2017
162 views
The number of even permutations of the multiset {1,1,2} is ___ .
0 votes
0 votes
2 answers
3
Vicky rix asked Mar 10, 2017
357 views
In how many ways can a group of n people be divided into pairs(2 people) ,given that n is an even number ?
0 votes
0 votes
1 answer
4
Sammohan Ganguly asked May 29, 2018
3,002 views
Among the integers $1,2,3,....,200$ if $101$ integers are chosen,then show that there are two among the chosen,such that one is divisible by the other.