English

How Many Different Words Can Be Formed with the Letters of Word 'Sunday'? How Many of the Words Begin with N? How Many Begin with N and End in Y?

Advertisements
Advertisements

Question

How many different words can be formed with the letters of word 'SUNDAY'? How many of the words begin with N? How many begin with N and end in Y?

Advertisements

Solution

Total number of words that can be formed with the letters of the word SUNDAY = 6! = 720
Now, if we fix the first letter as N, the remaining 5 places can be filled with the remaining 5 letters in 5! ways, i.e. 120.
If we fix the first letter as N and the last word as Y:
Remaining 4 places can be filled with 4 letters in 4! ways = 24

shaalaa.com
Factorial N (N!) Permutations and Combinations
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.4 [Page 37]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.4 | Q 5 | Page 37

RELATED QUESTIONS

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


If (n + 3)! = 56 [(n + 1)!], find n.


If P (n, 5) = 20. P(n, 3), find n ?


If P(11, r) = P (12, r − 1) find r.


Prove that:1 . P (1, 1) + 2 . P (2, 2) + 3 . P (3, 3) + ... + n . P (nn) = P (n + 1, n + 1) − 1.


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


From among the 36 teachers in a school, one principal and one vice-principal are to be appointed. In how many ways can this be done?


Four letters E, K, S and V, one in each, were purchased from a plastic warehouse. How many ordered pairs of letters, to be used as initials, can be formed from them?


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?


Find the number of different 4-letter words, with or without meanings, that can be formed from the letters of the word 'NUMBER'.


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


There are two works each of 3 volumes and two works each of 2 volumes; In how many ways can the 10 books be placed on a shelf so that the volumes of the same work are not separated?


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?


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?


All the letters of the word 'EAMCOT' are arranged in different possible ways. Find the number of arrangements in which no two vowels are adjacent to each other.


In how many ways can the letters of the word 'FAILURE' be arranged so that the consonants may occupy only odd positions?


In how many ways can the letters of the word 'STRANGE' be arranged so that

the vowels occupy only the odd places?


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

all consonants come together?


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:
SERIES


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?


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


How many permutations of the letters of the word 'MADHUBANI' do not begin with M but end with I?


If the permutations of a, b, c, d, e taken all together be written down in alphabetical order as in dictionary and numbered, find the rank of the permutation debac ?


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


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

 nCr + 2 · nCr − 1 + nCr − 2 = n + 2Cr.


Write the value of\[\sum^6_{r = 1} \ ^{56 - r}{}{C}_3 + \ ^ {50}{}{C}_4\]


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


Write the number of ways in which 12 boys may be divided into three groups of 4 boys each.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×