If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2+......+ ^{2017}C_{1008} = \lambda ^2 (\lambda > 0),$ then remainder when $\lambda $ is divided by $33$ is-
$8$
$13$
$17$
$25$
Determine $n$ if
$^{2 n} C_{3}:\,^{n} C_{3}=12: 1$
In an election there are $8$ candidates, out of which $5$ are to be choosen. If a voter may vote for any number of candidates but not greater than the number to be choosen, then in how many ways can a voter vote
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 no girl?
How many words, with or without meaning, can be formed using all the letters of the word $\mathrm{EQUATION}$ at a time so that the vowels and consonants occur together?
A total number of words which can be formed out of the letters $a,\;b,\;c,\;d,\;e,\;f$ taken $3$ together such that each word contains at least one vowel, is