Permutations and Combinations — JEE Main PYQs

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

Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${}^9{\mathrm{C}}_3$
Statement -2 : The number of ways of choosing any 3 places from 9 different places is ${}^9{\mathrm{C}}_3$.

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

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 nu …

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

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

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are of be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

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

The value of ${}^{50}{C}_4+{\sum }_{r=1}^6{}^{56-r}{C}_3$ is

The range of the function $f(x)={}^{7-x}{P}_{x-3}$ is

How many ways are there to arrange the letters in the word GARDEN with the vowels in alphabetical order?

The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is