Arrangements and Counting Principles Please respond to the f

Solution

Permutation V/S combination depends whether the order of the number matters or not

Let us suppose, i give you two tasks

First task, i want you to make a mix fruit salad made up of apple,banana and orange, then whichever fruit you put in the bowl first doesn\'t matter since the final end product fruit salad will be same.

Second task, now let us assume that someone wants to open a locker and i told him the key for the lock contains 2,3 and 5, will this thing matter?

Yes, since the locker will have only one combination out of 2,3,5 i.e. if we punch the three correct numbers at correct places then only we will be able to open a locker

A permutation is also defined as ordererd combination,

Example - Let us toss a coin six times and we want exactly 3 heads and 3 tails, then 3 heads and 3 tails can come in many fashion

HHHTTT

HTHHTT

HHTTTH

But if we want only specific combination i.e. all the head occurs first then that is the preferred combinatorial but the aim of problem is to count all the occurences then we need to sum up all the instances where three heads and three tails appear in the problem