Numbers of permutations of n things taken r at a time, when p things are always included, is

English

Gujarati

Hindi

6.Permutation and Combination

easy

The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is

$^n{C_r}\;p\;!$

$^{n - p}{C_r}\;r\;!$

$^{n - p}{C_{r - p}}\;r\;!$

None of these

Solution

(c) Since number of selections are $^{n – p}{C_{r – p}}.$ Therefore the arrangement of $r$ things can be done in $r$ ! ways. Hence the total permutations are $^{n – p}{C_{r – p}}\,r\,!$

Standard 11

Mathematics

Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is –

normal

If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is

easy

An engineer is required to visit a factory for exactly four days during the first $15$ days of every month and it is mandatory that no two visits take place on consecutive days. Then the number of all possible ways in which such visits to the factory can be made by the engineer during 1$-15$ June $2021$ is. . . . . .

medium

(IIT-2020)

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number

medium

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to

medium

(JEE MAIN-2023)

The numbers of permutations of $n$ things taken $r$ at a time, when $p$ things are always included, is

Solution

Similar Questions

Number of different words that can be formed from all letters of word $APPLICATION$ such that two vowels never come together is –

If $^8{C_r}{ = ^8}{C_{r + 2}}$, then the value of $^r{C_2}$ is

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ each digit appearing not more than once in each number

$\sum \limits_{ k =0}^6{ }^{51- k } C _3$ is equal to

Start a Free Trial Now