Combinations practice · Medium

A five digit number divisible by 6 is to be formed by using the digits $0,1,2,3,4$ and $8$ without repetition. The total number of ways in which this can be done is

The value of $\sum_{k=0}^{6}{ }^{51-k} C_{3}$ is

Seven people leave their bags outside temple and while returning after worshiping the deity, picked one bag each at random. In how many ways at least one and at most three of them get their correct bags?

If the total number of $m$ elements subsets of the set $A = \left\{ {{a_1},{a_2},{a_3}, \ldots {a_n}} \right\}$ is $\lambda$ times the number of 3 elements subsets containing ${a_4}$, then $n$ is

If $n$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $n$ is equal to:

A man $X$ has 7 friends, 4 of them are ladies and 3 are men. His wife $Y$ also has 7 friends, 3 of them are ladies and 4 are men. Assume and $Y$ have no common friends. Then, the total number of ways in which $X$ and $Y$ together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of $X$ and $Y$ are in this party, is

If $n \in N$, then value of the expression ${ }^{n-2} C_r+2 .^{n-2} C_{r-1}+{ }^{n-2} C_{r-2}=$

Number of ways in which 6 different toys can be distributed among two brothers in $1: 2$, is

Let $A$ be the set of 4 -digit numbers $a_{1} a_{2} a_{3} a_{4}$ where $a_{1} > a_{2} > a_{3} >$ $a_{4}$. Then $n(A)$ is equal to

If $a,\;b,\;c \in N,$ The anumber of points having position vector $a\mathbf{\hat i} + b\mathbf{\hat j} + c\mathbf{\hat k}$ such that $6 \le a + b + c \le 10$, is

A gentlemen hosts a party of $(m+n)$ guests and places ' $m$ ' at one round table and the remaining ' $n$ ' at the other round table. Number of ways the guests can be arranged is

If ${x}_{{k}} \geq 0, {k}=1,2,3,4,5$ and ${x}_1+{x}_2+{x}_3+{x}_4+{x}_5=20$ and ${x}_1+{x}_2+{x}_3=5$ then the number of integral solution of $\left(x_1, x_2, x_3, x_4, x_5\right)$

If $\sum\limits_{{r=1}}^n\left[\log _2 r\right]=1898$ (where [.] denotes greatest integer function), then number of zeroes at the end of $\mathrm{n}$ is/are

($n$!)! is divisible by

The number of ways in which 12 balls can be divided between two friends, one receiving 8 an the other 4, is

Statement 1: If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q>p$. Then the total number of functions from set $A$ to set $B$ is $q^{p}$.
[Online May 12, 2012]
Statement 2: The total number of selections of $p$ different objects out of $q$ objects is ${ }^{q} \mathrm{C}_{p}$.

Given 5 different green dyes, 4 different blue dyes and 3 different red dyes. The number of combinations of dyes that can be chosen by taking at least one green and one blue dye is

Find the number of three digit numbers which can be formed using the digits $0,1,2,2,3, 3,3 .$

Out of 10 consonants and 4 vowels, words with 6 consonants and 3 vowels are formed. The number of such words is

Let there are 6 shirts of different colours and 6 trousers of same colours as that of shirts. If the number of ways in which these can be put on by 5 men such that no men wear the shirt and the trouser of the same colour is $(k) 6!,$ then find the value of $k$.

The number of triangles which can be formed by using the vertices of a regular polygon of $\left( {n + 3} \right)$ sides is 220. Then $n$ is equal to

A student is allowed to select at most $n$ books from a collection of $\left( {2n + 1} \right)$ books. If the total number of ways in which he can select one book is 63, then the value of $n$ is equal to

The number of ways in which 13 gold coins can be distributed among three persons such that each one gets at least 2 gold coins is

Team A consists of 7 boys and n girls and team B has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n=

There are two parallel lines one having 10 point and other having 5 points. The number of triangle formed with vertice as these points

The number of ways in which four letters can be selected from the word degree is

The number of positive integers satisfying the inequality $n + {1_{{C_{n - 2}}}} - n + {1_{{C_{n - 1}}}} \le 50$ is

In how many ways can Rs 16 be divided into 4 persons when none of them get less than Rs 3?

The packs of 52 cards are shuffled together. The number of ways in which a man can be dealt 26 cards so that he does not get two cards of the same suit and same denomination, is

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