English

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

Advertisements
Advertisements

Question

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

Advertisements

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

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

RELATED QUESTIONS

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


Prove that:

\[\frac{(2n + 1)!}{n!}\] = 2n [1 · 3 · 5 ... (2n − 1) (2n + 1)]

If P (n, 4) = 12 . P (n, 2), find n.


If n +5Pn +1 =\[\frac{11 (n - 1)}{2}\]n +3Pn, find n.


In how many ways can five children stand in a queue?


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 words, with or without meaning, can be formed by using all the letters of the word 'DELHI', using each letter exactly once?


There are 6 items in column A and 6 items in column B. A student is asked to match each item in column A with an item in column B. How many possible, correct or incorrect, answers are there to this question?


In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?


If a denotes the number of permutations of (x + 2) things taken all at a time, b the number of permutations of x things taken 11 at a time and c the number of  permutations of x − 11 things taken all at a time such that a = 182 bc, find the value of x.


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?


How many words can be formed out of the letters of the word, 'ORIENTAL', so that the vowels always occupy the odd places?


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

there is no restriction on letters?


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

all consonants come together?


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 all letters are used but first is vowel.


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:

PAKISTAN


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

RUSSIA


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


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


In how many ways can the letters of the word 'ALGEBRA' be arranged without changing the relative order of the vowels and consonants?


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?


Find the number of numbers, greater than a million, that can be formed with the digits 2, 3, 0, 3, 4, 2, 3.


There are three copies each of 4 different books. In how many ways can they be arranged in a shelf?


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?


In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?


If the letters of the word 'LATE' be permuted and the words so formed be arranged as in a dictionary, find the rank of the word LATE.


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


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


Prove that: 4nC2n : 2nCn = [1 · 3 · 5 ... (4n − 1)] : [1 · 3 · 5 ... (2n − 1)]2.


Let r and n be positive integers such that 1 ≤ r ≤ n. Then prove the following:

\[\frac{^{n}{}{C}_r}{^{n - 1}{}{C}_{r - 1}} = \frac{n}{r}\]

How many words, with or without meaning can be formed from the letters of the word 'MONDAY', assuming that no letter is repeated, if all letters are used but first letter is a vowel?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×