Permutations and Combinations Questions

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

If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in a dictionary, then the word SACHIN appears at serial number:

A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is:

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by:

In a shop there are five types of ice-creams available. A child buys six ice-creams.Statement - 1: The number of different ways the child can buy the six ice-creams is ${}^{10}{C}_5$.Statement - 2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6$ A’s and $4$ B’s in a row.

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is: