A set contains $2n + 1$ elements. The number of subsets of this set containing more than $n$ elements is equal to

- A
${2^{n - 1}}$

- B
${2^n}$

- C
${2^{n + 1}}$

- D
${2^{2n}}$

If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then

$^{20}C_1 + 3 ^{20}C_2 + 3 ^{20}C_3 + ^{20}C_4$ is equal to-

The total number of natural numbers of six digits that can be made with digits $1, 2, 3, 4$, if all digits are to appear in the same number at least once, is

Out of $6$ books, in how many ways can a set of one or more books be chosen

The number of ways in which four letters of the word $‘MATHEMATICS$’ can be arranged is given by