हिंदी

How Many Different Numbers, Greater than 50000 Can Be Formed with the Digits 0, 1, 1, 5, 9. - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

Numbers greater than 50000 can either have 5 or 9 in the first place and will consist of 5 digits.
Number of arrangements having 5 as the first digit =\[\frac{4!}{2!}\]

Number of arrangement having 9 as the first digit =\[\frac{4!}{2!}\]

∴ Required arrangements =\[\frac{4!}{2!}\]+\[\frac{4!}{2!}\]=24

shaalaa.com
Factorial N (N!) Permutations and Combinations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.5 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.5 | Q 11 | पृष्ठ ४३

संबंधित प्रश्न

Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)


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


Prove that: 

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

Prove that:

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


Prove that:

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

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


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 words, with or without meaning, can be formed by using the letters of the word 'TRIANGLE'?


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.


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?


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?


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


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
each word begins with E?


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

each word begins with O and ends with L?


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:

RUSSIA


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:
EXERCISES


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 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 number of four digits can be formed with the digits 1, 3, 3, 0?


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


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


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.


Find the total number of ways in which six ‘+’ and four ‘−’ signs can be arranged in a line such that no two ‘−’ signs occur together.


The letters of the word 'ZENITH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENITH'?


For all positive integers n, show that 2nCn + 2nCn − 1 = `1/2` 2n + 2Cn+1 


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


Find the number of permutations of n distinct things taken together, in which 3 particular things must occur together.


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


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×