Six students are contesting the election for the president ship of the

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