Recent questions tagged counting

In a group of $120$ people: $65$ eat Rice, $45$ eat bread, $42$ eat curd, $20$ eat both Rice and bread, $25$ eat both Rice and curd, $15$ eat both bread and curd, and $8$...

In a pack of $42$ cards, $3$ cards are chosen one after the other. Find the number of ways this can be done without replacement:$1722$$1752$$68880$$6880$

Match List - I with List - II.$\begin{array}{|ll|ll|} \hline & \textbf{List - I} &&\textbf{List - II} \\ & \textbf{(Queries)} && \textbf{(Probability)} \\ \hline (A) & \...

The number of straight lines that can be drawn out of $12$ points of which $8$ are collinear is:$39$$29$$49$$59$ 

The sum of all the $4$ digit numbers that can be formed with the digits $3,4,5$ and $6$ is:$119988$$11988$$191988$None of the options 

Consider a complete graph $\text{G}$ with $4$ vertices. The graph $\text{G}$ has _______ spanning trees.$15$$8$$16$$13$

In how many ways can $10$ identical chocolate bars be distributed among $5$ children, in such a way that each child gets at least one chocolate bar?$50$$126$$252$$3125$

How many positive integers less than $1000$ are neither divisible by $3$ nor divisible by $5$? Explain how you arrived at your answer.

How many distinct ways are there to paint the $6$ faces of a cube using six colors $( 1, 2,3,4,5,6)$, with each face painted a different color, such that no two painted c...

How many $8-permutations$ are there of the $10$ $letters$ of the word $CALIFORNIA$ (with repeated letters)?A. $\frac{47}{4} \cdot 8$ !B. $\frac{47}{2} \cdot 8$ !C. $8!\cd...

Is it $True$ or $False$, if $51$ integers are chosen from the set $S=\{1,2, \ldots, 100\}$, then there is always a pair of chosen integers which differ by $1$ . $True$$Fa...

A bakery sells exactly $5$ kinds of cookies including chocolate-chip cookies and shortbread cookies. Assuming that the bakery has at least $10$ cookies of each kind, how ...

Seven people, including two who do not want to sit next to each other, are to be seated at a round table. How many (circular) arrangements are there?

How many ways are there to form a $3-letter$ word (i.e. sequence) containing the letter $C$ using the letters $A, B, C, D, E$ with repetitions of letters allowed?

There are $10$ points on a plane in such a way that $6$ of these points are collinear and other than these $6$ points, no set of $3$ or more points are collinear. The num...

Twelve monkeys have collected a total of $N$ bananas where every monkey has managed to collect at least one banana. What is the maximum value of $N$ for which you can gua...

Five marbles of different sizes are to be coloured using the three colours, namely red, yellow and blue, where each marble is coloured with exactly one colour. The number...