$A$ box contains two white balls,three black balls,and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw?

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

How many words (with or without meaning) of $3$ distinct English alphabets can be formed?

We are to form different words with the letters of the word $INTEGER$. Let $m_1$ be the number of words in which $I$ and $N$ are never together and $m_2$ be the number of words which begin with $I$ and end with $R$,then $m_1/m_2$ is equal to

The set $S = \{1, 2, 3, \ldots, 12\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus $A \cup B \cup C = S$ and $A \cap B = B \cap C = C \cap A = \emptyset$. The number of ways to partition $S$ is

How many $2$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5$ and $8$,if repetition of digits is allowed?