Amit M Agarwal Solutions for Chapter: Permutation and Combination, Exercise 8: Entrances Gallery

A teacher takes $3$ children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more that a particular child goes to the zoo. The number of children in her class is

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 at least one book is $225$, then the value of $n$ is

In how many ways can $5$ prizes be distributed among four students, when every student can take one or more prizes?

The number of ways in which the digits $1, 2, 3, 4, 3, 2, 1$ can be arranged so that the odd digits always occupy the odd places,is

If ${}^{56}P_{r+6}:{}^{54}P_{r+3}=30800:1,$ then the value of $r$ is

The number of permutations by taking all letters and keeping the vowels of the word $\text{'}\mathrm{COMBINE}\text{'}$ in the odd places, is

From $12$ books, the difference between number of ways of selection of $5$ books when one specified book is always excluded and one specified book is always included, is

If ${}^{n-1}C_3+{}^{n-1}C_4>{}^{n}C_3,$ then $n$ is just greater than integer