मराठी

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

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.4 [पृष्ठ ३६]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.4 | Q 3 | पृष्ठ ३६

संबंधित प्रश्‍न

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)


Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)


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


If (n + 2)! = 60 [(n − 1)!], find n. 


Prove that: 

\[\frac{n!}{(n - r)!}\] = n (n − 1) (n − 2) ... (n − (r − 1))

Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]


If P (9, r) = 3024, find r.


If P (n, 4) = 12 . P (n, 2), find n.


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


If P (n, 5) : P (n, 3) = 2 : 1, find n.


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?


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?


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?


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 'STRANGE' be arranged so that

the vowels occupy only the odd places?


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 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?


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

all vowels come together?


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


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 at a time.


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

RUSSIA


How many different signals can be made from 4 red, 2 white and 3 green flags by arranging all of them vertically on a flagstaff?


How many words can be formed from the letters of the word 'SERIES' which start with S and end with S?


Find the total number of permutations of the letters of the word 'INSTITUTE'.


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


Evaluate

\[^ {20}{}{C}_5 + \sum^5_{r = 2} {}^{25 - r} C_4\]

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

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

There are 10 persons named\[P_1 , P_2 , P_3 , . . . . , P_{10}\]
Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.


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?


If 35Cn +7 = 35C4n − 2 , then write the values of n.


Write the expression nCr +1 + nCr − 1 + 2 × nCr in the simplest form.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×