Question:
Six students are contesting the election for the president ship of the students, union. In how many ways can their names be listed on the ballot papers?
Solution:
To find: number of arrangements of names on a ballot paper.
There are six contestants contesting in the elections.
Name of any 1 student out of six can appear first on the ballot paper.
2 position on the ballot paper can be filled by rest of the five names and so on.
Formula:
Number of permutations of $n$ distinct objects among $r$ different places, where repetition is not allowed, is
$P(n, r)=n ! /(n-r) !$
Therefore, permutation of 6 different objects in 6 places is
$P(6,6)=\frac{6 !}{(6-6) !}$
$=\frac{6 !}{0 !}=\frac{720}{1}=720$
Hence, their name can be arranged in 720 ways