English

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

Advertisements
Advertisements

Question

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

Sum
Advertisements

Solution

when n = 6, r = 2  `(n!)/((n-r)!) = (6!)/((6 - 2)!) = (6!)/(4!) = (6  xx  5  xx  4!)/(4!) = 30` 

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Permutations and Combinations - EXERCISE 6.2 [Page 107]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 6 Permutations and Combinations
EXERCISE 6.2 | Q 5. (i) | Page 107

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?


Find n if n – 1P3 : nP4 = 1 : 9


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


Find x in each of the following:

\[\frac{1}{6!} + \frac{1}{7!} = \frac{x}{8!}\]

How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?


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 ?


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


Write the number of words that can be formed out of the letters of the word 'COMMITTEE' ?


The number of arrangements of the word "DELHI" in which E precedes I 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 six-digit telephone numbers can be formed if the first two digits are 45 and no digit can appear more than once?


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?


  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?

The possible outcomes when a coin is tossed five times:


The number of permutation of n different things taken r at a time, when the repetition is allowed 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?


A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?


8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?


Find the distinct permutations of the letters of the word MISSISSIPPI?


In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together


Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?


Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?


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


Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?


How many words can be formed with the letters of the word MANAGEMENT by rearranging them?


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.


Find the number of permutations of n different things taken r at a time such that two specific things occur together.


Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.


Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together


The number of 5-digit telephone numbers having atleast one of their digits repeated 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 the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.


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


8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×