English

Evaluate n!(n-r)!, when n = 9, r = 5 - Mathematics

Advertisements
Advertisements

Question

Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5

Sum
Advertisements

Solution

When n = 9, r = 5  `(n!)/((n-r)!)  = (9!)/((9 - 5)!) = (9!)/(4!) = (9  xx 8  xx 7  xx 6  xx  5  xx  4!)/(4!)`

= 9 x 8 x 7 x 6 x 5 = 15120 

shaalaa.com
  Is there an error in this question or solution?
Chapter 7: Permutations and Combinations - Exercise 7.2 [Page 141]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 7 Permutations and Combinations
Exercise 7.2 | Q 5.2 | Page 141

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate 8!


How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?


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


Find r if `""^5P_r = ""^6P_(r-1)`


In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.


Which of the following are true:

(2 × 3)! = 2! × 3!


Find the number of ways in which 8 distinct toys can be distributed among 5 childrens.


In how many ways can 5 different balls be distributed among three boxes?


There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?


Evaluate each of the following:

8P3


Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?


Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?


Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is


The number of arrangements of the letters of the word BHARAT taking 3 at a time is


In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is


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


If nP4 = 12(nP2), find n.


In how many ways 5 boys and 3 girls can be seated in a row, so that no two girls are together?


  1. In how many ways can 8 identical beads be strung on a necklace?
  2. In how many ways can 8 boys form a ring?

Evaluate the following.

`((3!)! xx 2!)/(5!)`


The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:


If `""^(("n"  – 1))"P"_3 : ""^"n""P"_4` = 1 : 10 find n


Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?


In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?


How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together


How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together


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


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 never together.


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.


The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.


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


The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place 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 ______.


How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

C1 C2
(a) 4 letters are used at a time (i) 720
(b) All letters are used at a time (ii) 240
(c) All letters are used but the first is a vowel (iii) 360

The number of three-digit even numbers, formed by the digits 0, 1, 3, 4, 6, 7 if the repetition of digits is not allowed, is ______.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×