हिंदी

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? - Mathematics

Advertisements
Advertisements

प्रश्न

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?

Advertisements

उत्तर

If we fix the first letter as P and the last letter as I, the remaining 8 letters can be arranged in 8! ways to form the words.
∴  Number of words that start with P and end with I = 8!

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.4 [पृष्ठ ३७]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.4 | Q 6.3 | पृष्ठ ३७

संबंधित प्रश्न

If (n + 2)! = 60 [(n − 1)!], find n. 


If (n + 3)! = 56 [(n + 1)!], find n.


Prove that:

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


If nP4 = 360, find the value of n.


If P (9, r) = 3024, find r.


If P(11, r) = P (12, r − 1) find r.


If P (2n − 1, n) : P (2n + 1, n − 1) = 22 : 7 find n.


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.


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 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?


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.


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


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 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 vowels always occupy even places?


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

there is no restriction on letters?


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 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


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 numbers can be formed with the digits 1, 2, 3, 4, 3, 2, 1 so that the odd digits always occupy the odd places?


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 numbers, greater than 50000 can be formed with the digits 0, 1, 1, 5, 9.


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


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?


The letters of the word 'SURITI' are written in all possible orders and these words are written out as in a dictionary. Find the rank of the word 'SURITI'.


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?


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:

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

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 number of diagonals of an n-sided polygon.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×