General illustration or permutation OF different object, grouping

Permutations

Permutations

Permutation OF Identical Objects

Permutation OF Identical Objects

illustration on same & difference OF itf

Illustration Based upon Formation OF Groups

Illustration Based upon Formation OF Groups

The number of permutation of n different objects, taken r at a line, when repetitions are allowed, is …….. .

Prove that the no.of permutations of n different objects taken r at a time in which two specified objects always occur together 2!(r-1)(n-2)P_(r-2)

Prove that the no.of all permutations of n different objects taken r at a time when a particular object is to be always included in each arrangement is r.(n-1)P_(r-1)