The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently is

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