मराठी

How Many 3-digit Numbers Can Be Formed by Using the Digits 1 to 9 If No Digit is Repeated?

Advertisements
Advertisements

प्रश्न

How many 3-digit numbers can be formed by using the digits 1 to 9 if no digit is repeated?

Advertisements

उत्तर

Total number of arrangements of 9 digits, taken 3 at a time = 9P3
∴ Total 3-digit numbers that can be formed by using the digits 1 to 9, if no digit is repeated = 9P3 = `9xx8xx7=504`

shaalaa.com
Factorial N (N!) Permutations and Combinations
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 16: Permutations - Exercise 16.3 [पृष्ठ २९]

APPEARS IN

आर.डी. शर्मा Mathematics [English] Class 11
पाठ 16 Permutations
Exercise 16.3 | Q 29 | पृष्ठ २९

संबंधित प्रश्‍न

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10


If (n + 1)! = 90 [(n − 1)!], find n.


Prove that: 

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

If P (n, 4) = 12 . P (n, 2), find n.


If P (n − 1, 3) : P (n, 4) = 1 : 9, 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.


In how many ways can five children stand in a queue?


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 all the letters of the word 'DELHI', using each letter exactly once?


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

there is no restriction on letters?


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

all vowels come together?


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 all letters are used but first is vowel.


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


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


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


How many words can be formed by arranging the letters of the word 'MUMBAI' so that all M's come together?


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?


In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same colour are indistinguishable?


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 relative order of vowels and consonants do not alter?


Prove that the product of 2n consecutive negative integers is divisible by (2n)!


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:
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.


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


Write the maximum number of points of intersection of 8 straight lines in a plane.


Write the number of ways in which 5 red and 4 white balls can be drawn from a bag containing 10 red and 8 white balls.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×