A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to
${2^{n - 1}}$
${2^n}$
${2^{n + 1}}$
${2^{2n}}$
The number of words (with or without meaning) that can be formed from all the letters of the word $"LETTER"$ in which vowels never come together is
The number of matrices of order $3 \times 3$, whose entries are either $0$ or $1$ and the sum of all the entries is a prime number, is$....$
The number of ways in which thirty five apples can be distributed among $3$ boys so that each can have any number of apples, is
From a class of $25$ students, $10$ are to be chosen for an excursion party. There are $3$ students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is $........$