Recent questions tagged goclasses-combinatorics-practice-questions

What is the minimum number of elements that must be selected from the set $\{1,2,3, \ldots, 50\}$ to ensure that at least two of them are consecutive?

How many arrangements of the digits $0,1, \ldots, 9$ are there that do not end with a $1$ and do not begin with a $9$ ?

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at $440{ }^{\text {th }}$ position...

How many permutations of the set $T_{10}=\{1,2, \ldots, 10\}$ are there which begin with an odd number?

Let $A=\{1,2,3, \ldots, 18\}$. Four mutually distinct elements $x_1, x_2, x_3, x_4 \in A$ are selected.Determine the minimum positive integer $y$ such that no matter whic...

From a group of $7$ batsmen and $6$ bowlers, $10$ players are to be chosen for a team, which should include atleast $4$ batsmen and atleast $4$ bowlers. One batsmen and o...

A bag contains $100$ apples, $100$ oranges, $100$ bananas and $100$ pears. Every minute you choose one fruit from the bag. How long will it take to ensure that you have a...

How many combinations with repetitions for $4$ numbers are there from the set $\{1,2,3,4,5,6\}$ ?

Group $A$ consists of $7$ boys and $3$ girls, while group $B$ consists of $6$ boys and $5$ girls. The number of ways, $4$ boys and $4$ girls can be invited for a picnic i...

How many natural numbers between $1$ and $600$ are there which are multiples of $2$ or $3$ ?

Let the sequence $\left\{a_n\right\}$ be defined by:$$a_0=1, \quad a_1=6, \quad \text { and } \quad a_{n+1}=6 a_n-9 a_{n-1} \text { for } n \geq 1 .$$Which of the followi...

The number of 6 -letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear a...

Compute the number of all possible rearrangements of the following sequence of letters$$A A A B B B C C C$$such that no three identical consecutive letters exist (that is...

Q1. Let $A$ be a subset of $n+1$ numbers chosen from the set $\{1,2,3, \ldots, 2 n\}$, where $n$ is a natural number. Which of the following must be true?All elements in ...

The number of sequences of ten terms, whose terms are either 0 or 1 or 2 , that contain exactly five 1 s and exactly three 2 s , is equal to:$360$ $2520$ $1820$ $45$