Let $${T_n}$$ denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If $${T_{n + 1}} - {T_n} = 21$$, then n equals

How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions?

A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The total number of ways this can be done is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the numbers of words which have at least one letter repeated are