Fundamental Principle of Counting
* If an event can occur in m different ways, following which another event can occur in n different ways, then the total number of the occurrence of the events in the
given order is m × n.
Introduction to Permutation
* A permutation is an arrangement in a definite order of a number of objects taken some or all at a time.
* The number of permutations of n different objects taken r at a time is equal to nPr,
where 0 < r ≤ n.
Permutations
* The number of permutations of n distinct objects taken r at a time, where repetition of the objects is allowed, is nr.
* The number of permutations of n objects, where p objects are of the same kind, and the rest are all different, is \frac{n!}{ p_{1} ! }.
* The number of permutations of n objects n objects, where p1 objects are of one kind, p2 are of the kth kind,…., pk are of the kth kind, and the rest, if any,
Are of a different kind, is \frac{n!}{ p_{1} ! \thinspace \thinspace \thinspace p_{2}!...... \thinspace \thinspace \thinspace p_{k} ! }
Introduction to Combinations
* In a combination, the order is not important.
nCr × r! = nPr.
Theorem on Combinations
nPr = nCr × r!
nCr =nCn – r
nCa=nCb, then either a = b or n = a + b
nCr+ nCr– 1 =n+1Cr