Out of $6$ books, in how many ways can a set of one or more books be chosen
$64$
$63$
$62$
$65$
(b) Required number of ways
$=^6{C_1}+^6{C_2}+^6{C_3}+^6{C_4}+^6{C_5}+^6{C_6}=2^6-1=63$.
If $^{n + 1}{C_3} = 2{\,^n}{C_2},$ then $n =$
Total number of $6-$digit numbers in which only and all the five digits $1,3,5,7$ and $9$ appear, is
A group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least $3$ girls $?$
If all the letters of the word $'GANGARAM'$ be arranged, then number of words in which exactly two vowels are together but no two $'G'$ occur together is-
The number of ways in which $3$ children can distribute $10$ tickets out of $15$ consecutively numbered tickets themselves such that they get consecutive blocks of $5, 3 $ and $2$ tickets is
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