English

How Many Different Numbers of Six Digits Can Be Formed from the Digits 3, 1, 7, 0, 9, 5 When Repetition of Digits is Not Allowed?

Advertisements
Advertisements

Question

How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?

Advertisements

Solution

The first digit cannot be zero. Thus, the first digit can be filled in 5 ways.
Number of ways for filling the second digit = 5
(as repetition of digits is not allowed)
Number of ways for filling the third digit = 4
Number of ways for filling the fourth digit = 3
Number of ways for filling the fifth digit = 2
Number of ways for filling the sixth digit = 1
Total numbers = `5xx5xx4xx3xx2xx1= 600`

shaalaa.com
  Is there an error in this question or solution?
Chapter 16: Permutations - Exercise 16.2 [Page 15]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.2 | Q 27 | Page 15

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Determine n if  `""^(2n)C_3 : ""^nC_3 = 11: 1`


In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?


Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.


In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


Compute: 

(i)\[\frac{30!}{28!}\]


Compute:

 L.C.M. (6!, 7!, 8!)


A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?


How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?


How many three-digit odd numbers are there?


In how many ways can six persons be seated in a row?


How many 3-digit numbers are there, with distinct digits, with each digit odd?


Evaluate the following:

14C3


If n +2C8 : n − 2P4 = 57 : 16, find n.


If 28C2r : 24C2r − 4 = 225 : 11, find r.


A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?


In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.


Find the number of diagonals of (ii) a polygon of 16 sides.


In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?


In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?


In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?


A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?


Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.


A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?


Write \[\sum^m_{r = 0} \ ^{n + r}{}{C}_r\] in the simplified form.


There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.


If\[\ ^{( a^2 - a)}{}{C}_2 = \ ^{( a^2 - a)}{}{C}_4\] , then a =


Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to


Given 11 points, of which 5 lie on one circle, other than these 5, no 4 lie on one circle. Then the number of circles that can be drawn so that each contains at least 3 of the given points is


Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.


Find the value of 20C1619C16 


A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Mathematics Part II, unless Mathematics Part I is also borrowed. In how many ways can he choose the three books to be borrowed?


A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they can be of any colour


A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls


If nC12 = nC8, then n is equal to ______.


Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.


The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.


A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.


To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.


If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.


There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×