JEE Advanced · 2007 · 08 Apr 2007 · Paper 2 · Permutations and Combinations

The number of ways to distribute 10 identical red pens and 14 identical blue pens among four persons such that each person gets 6 pens, is ____.

Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0,1 and 2 . For example, 2210222 is in $S$, but 0210222 is NOT in $S$.

Then the number of elements $x$ in $S$ such that at least one the digits 0 and 1 appears exactly twice in $x$, is …

Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties.
i. $R$ has exactly 6 elements.
ii. For each $(a,b)\in R$, we have $|a-b|\ge 2$.
Let $Y=\{R\in X$ : The range of $R$ has exactly one element $\}$ and …

Let $S=\{1,2,3,4,5,6\}$ and $X$ be the set of all relations $R$ from $S$ to $S$ that satisfy both the following properties.
i. R has exactly 6 elements.
ii. For each $(a,b)\in R$, we have $|a-b|\ge 2$.

Let $Y=\{R\in X$ : The range of R has exactly one element $\}$ and …

A group of 9 students, ${\mathrm{s}}_1,{\mathrm{s}}_2,\dots ..,{\mathrm{s}}_9$, is to be divided to from three teams X, Y, and Z of sizes 2, 3, and 4, respectively. Suppose that ${\mathrm{s}}_1$ cannot be selected for the team X, and ${\mathrm{s}}_2$ cannot be selecte …

The number of 4-digit integers in the closed interval [2022, 4482] formed by using the digits $0,2,3,4,6,7$ is ____.