English

How Many Words Can Be Formed from the Letters of the Word 'Sunday'? How Many of These Begin with D? - Mathematics

Advertisements
Advertisements

Question

How many words can be formed from the letters of the word 'SUNDAY'? How many of these begin with D?

Solution

Total number of words that can be formed with the letters of the word SUNDAY = 6! = 720
Fixing the first letter as D:
Number of arrangements of the remaining 5 letters, taken 5 at a time = 5! = 120
Number of words with the starting letter D = 120

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.4 [Page 36]

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 3 | Page 36

RELATED QUESTIONS

Prove that: n! (n + 2) = n! + (n + 1)!


If (n + 1)! = 90 [(n − 1)!], find n.


If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

 

 


If 5 P(4, n) = 6. P (5, n − 1), find n ?


If P(11, r) = P (12, r − 1) find r.


If P (n − 1, 3) : P (n, 4) = 1 : 9, find n.


If P (15, r − 1) : P (16, r − 2) = 3 : 4, find r.


Four books, one each in Chemistry, Physics, Biology and Mathematics, are to be arranged in a shelf. In how many ways can this be done?


How many three-digit numbers are there, with distinct digits, with each digit odd?


How many three-digit numbers are there, with no digit repeated?


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


How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letter G always occupies the first place?


How many different words can be formed from the letters of the word 'GANESHPURI'? In how many of these words:

the letters P and I respectively occupy first and last place?


How many permutations can be formed by the letters of the word, 'VOWELS', when

each word begins with O and ends with L?


How many words can be formed out of the letters of the word 'ARTICLE', so that vowels occupy even places?


In how many ways can a lawn tennis mixed double be made up from seven married couples if no husband and wife play in the same set?


How many words (with or without dictionary meaning) can be made from the letters in the word MONDAY, assuming that no letter is repeated, if 4 letters are used at a time?


Find the number of words formed by permuting all the letters of the following words:
INDEPENDENCE


Find the number of words formed by permuting all the letters of the following words:
INTERMEDIATE


Find the number of words formed by permuting all the letters of the following words:
ARRANGE


Find the number of words formed by permuting all the letters of the following words:

RUSSIA


How many words can be formed with the letters of the word 'PARALLEL' so that all L's do not come together?


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


How many number of four digits can be formed with the digits 1, 3, 3, 0?


In how many ways can the letters of the word 'ARRANGE' be arranged so that the two R's are never together?


How many different arrangements can be made by using all the letters in the word 'MATHEMATICS'. How many of them begin with C? How many of them begin with T?


A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?


How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?


In how many ways can the letters of the word
"INTERMEDIATE" be arranged so that:the vowels always occupy even places?


In how many ways can the letters of the word "INTERMEDIATE" be arranged so that:

the relative order of vowels and consonants do not alter?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:
n · n − 1Cr − 1 = (n − r + 1) nCr − 1


How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if (i) 4 letters are used at a time 


How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?


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


Write the number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×