मराठी

The Number of Permutations of N Different Things Taking R at a Time When 3 Particular Things Are to Be Included Isn − 3pr − 3,N − 3pr,Npr − 3,R ! N − 3cr − 3 - Mathematics

Advertisements
Advertisements

प्रश्न

The number of permutations of n different things taking r at a time when 3 particular things are to be included is

पर्याय

  • n − 3Pr − 3

  •  n − 3Pr

  • nPr − 3

  • r ! n − 3Cr − 3

MCQ
Advertisements

उत्तर

r ! n − 3Cr − 3

Here, we have to permute n things of which 3 things are to be included.
So, only the remaining (n - 3) things are left for permutation, taking (r - 3) things at a time. This is because 3 things have already been included.

But, these r things can be arranged in r! ways.
∴ Total number of permutations = r ! n − 3Cr − 3
shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.7 [पृष्ठ ४६]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.7 | Q 1 | पृष्ठ ४६

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Evaluate 8!


Compute `(8!)/(6! xx 2!)`


Evaluate `(n!)/((n-r)!)` when  n = 6, r = 2 


How many 4-digit numbers are there with no digit repeated?


Find r if `""^5P_r = 2^6 P_(r-1)`


In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.


A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.


How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?


Evaluate each of the following:

P(6, 4)


In how many ways can 4 letters be posted in 5 letter boxes?


Write the number of arrangements of the letters of the word BANANA in which two N's come together.


Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?


The number of five-digit telephone numbers having at least one of their digits repeated is


The number of arrangements of the word "DELHI" in which E precedes I is


The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is


The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is


If nP4 = 12(nP2), find n.


How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?


Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.


For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:


8 women and 6 men are standing in a line. How many arrangements are possible if any individual can stand in any position?


8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?


A coin is tossed 8 times, how many different sequences of heads and tails are possible?


How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative


If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
GARDEN


If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY


Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are


Choose the correct alternative:
The product of r consecutive positive integers is divisible b


The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.


In how many ways can 5 children be arranged in a line such that two particular children of them are always together 


If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?


In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.


Suppose m men and n women are to be seated in a row so that no two women sit together. If m > n, show that the number of ways in which they can be seated is `(m!(m + 1)!)/((m - n + 1)1)`


There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.


The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.


The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.


Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:

C1 C2
(a) Boys and girls alternate: (i) 5! × 6!
(b) No two girls sit together : (ii) 10! – 5! 6!
(c) All the girls sit together (iii) (5!)2 + (5!)2
(d) All the girls are never together : (iv) 2! 5! 5!

If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×