English

Evaluate Each of the Following:6p6

Advertisements
Advertisements

Question

Evaluate each of the following:

6P

Advertisements

Solution

\[{}^6 P_6 = \frac{6!}{(6 - 6)!} \]
\[ = \frac{6!}{0!} \]
\[ = \frac{6!}{1}                 (\text{Since} , 0! = 1) \]
\[ = 720\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.3 [Page 28]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.3 | Q 1.3 | Page 28

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate 4! – 3!


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


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


Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?


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?


Which of the following are true:

(2 × 3)! = 2! × 3!


How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?


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


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:

10P

Evaluate each of the following:

P(6, 4)


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


Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.


Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?


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


If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is


If k + 5Pk + 1 =\[\frac{11 (k - 1)}{2}\]. k + 3Pk , then the values of k are


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


Find x if `1/(6!) + 1/(7!) = x/(8!)`


Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.


How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?


Evaluate the following.

`(3! xx 0! + 0!)/(2!)`


If n is a positive integer, then the number of terms in the expansion of (x + a)n is:


The total number of 9 digit number which has all different digit is:


If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r


A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?


A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.

What is the maximum number of different answers can the students give?


How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?


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


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


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 distinct 6-digit numbers are there?


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


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


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


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 ______.


If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.


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 ______.


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×