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?

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

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


If P (5, r) = P (6, r − 1), find r ?


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


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


If P (n, 5) : P (n, 3) = 2 : 1, 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 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?


How many 3-digit even number can be made using the digits 1, 2, 3, 4, 5, 6, 7, if no digits is repeated?


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

the vowels come together?

 


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 are always together?


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


m men and n women are to be seated in a row so that no two women sit together. if m > n then show that the number of ways in which they can be seated as\[\frac{m! (m + 1)!}{(m - n + 1) !}\]


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.


How many three letter words can be made using the letters of the word 'ORIENTAL'?


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:
SERIES


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


Find the total number of arrangements of the letters in the expression a3 b2 c4 when written at full length.


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


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


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?


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'.


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 relative order of vowels and consonants do not alter?


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:

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

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:

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

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

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


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?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×