Out of $6$ books, in how many ways can a set of one or more books be chosen
$64$
$63$
$62$
$65$
In how many ways can $21$ English and $19$ Hindi books be placed in a row so that no two Hindi books are together
The English alphabet has $5$ vowels and $21$ consonants. How many words with two different vowels and $2$ different consonants can be formed from the alphabet?
The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
If $^{n} C _{9}=\,\,^{n} C _{8},$ find $^{n} C _{17}$
In a shop there are five types of ice-creams available. A child buys six ice-creams.
Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$
Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.