Topic: Permutations are solved when all the objects are distinct
Question: How to Permutations are solved when all the objects are distinct?
Answer: The number of permutations of n different objects taken r at a time,
where 0 < r ≤ n and the objects do not repeat is n ( n – 1) ( n – 2). . .( n – r + 1), which is denoted by nPr. Proof There will be as many permutations as there are ways of filling in r vacant
places . . . by ← r vacant places →
the n objects. The first place can be filled in n ways; following which, the second place
can be filled in (n – 1) ways, following which the third place can be filled in (n – 2)
ways,..., the rth place can be filled in (n – (r – 1)) ways. Therefore, the number of
ways of filling in r vacant places in succession is n(n – 1) (n – 2) . . . (n – (r – 1)) or
n ( n – 1) (n – 2) ... (n – r + 1)
This expression for nPr is cumbersome and we need a notation which will help to
reduce the size of this expression. The symbol n! (read as factorial n or n factorial )
comes to our rescue. In the following text we will learn what actually n! means.
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