The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is
- A
$^n{C_r}\;p\;!$
- B
$^{n - p}{C_r}\;r\;!$
- C
$^{n - p}{C_{r - p}}\;r\;!$
- D
None of these
Similar Questions
There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit
There are $9$ chairs in a room on which $6$ persons are to be seated, out of which one is guest with one specific chair. In how many ways they can sit
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 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$....$
- [JEE MAIN 2022]
The number of arrangements that can be formed from the letters $a, b, c, d, e,f$ taken $3$ at a time without repetition and each arrangement containing at least one vowel, is
The number of arrangements that can be formed from the letters $a, b, c, d, e,f$ taken $3$ at a time without repetition and each arrangement containing at least one vowel, is
- [AIEEE 2012]
Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.
Determine the number of $5$ card combinations out of a deck of $52$ cards if there is exactly one ace in each combination.
How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels
How many words can be formed by taking $3$ consonants and $2$ vowels out of $5$ consonants and $4$ vowels