English

How Many Different Numbers of Six Digits Each Can Be Formed from the Digits 4, 5, 6, 7, 8, 9 When Repetition of Digits is Not Allowed? - Mathematics

Advertisements
Advertisements

Question

How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?

Solution

Number of ways of filling the first digit = 6
Number of ways of filling the second digit = 5
(as repetition is not allowed)
Number of ways of filling the third digit = 4
Number of ways of filling the fourth digit =3
Number of ways of filling the fifth digit = 2
Number of ways of filling the sixth digit = 1
Total numbers = `6xx5xx4xx3xx2xx1=720`

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

APPEARS IN

RD Sharma Mathematics [English] Class 11
Chapter 16 Permutations
Exercise 16.2 | Q 26 | Page 15

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?


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:

(i) exactly 3 girls?

(ii) atleast 3 girls?

(iii) atmost 3 girls?


Prove that

\[\frac{1}{9!} + \frac{1}{10!} + \frac{1}{11!} = \frac{122}{11!}\]

How many three-digit numbers are there with no digit repeated?


A number lock on a suitcase has 3 wheels each labelled with ten digits 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.


If nC10 = nC12, find 23Cn.


If 8Cr − 7C3 = 7C2, find r.


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


From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer


A sports team of 11 students is to be constituted, choosing at least 5 from class XI and at least 5 from class XII. If there are 20 students in each of these classes, in how many ways can the teams be constituted?


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


Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.


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?


How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?


How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?


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


In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?


There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?


If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to


Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?


Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120


Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.


All the letters of the word ‘EAMCOT’ are arranged in different possible ways. The number of such arrangements in which no two vowels are adjacent to each other is ______.


The straight lines l1, l2 and l3 are parallel and lie in the same plane. A total numbers of m points are taken on l1; n points on l2, k points on l3. The maximum number of triangles formed with vertices at these points are ______.


We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?


A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw


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.


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 must all be of the same colour.


Everybody in a room shakes hands with everybody else. The total number of handshakes is 66. The total number of persons in the room is ______.


The number of ways in which we can choose a committee from four men and six women so that the committee includes at least two men and exactly twice as many women as men is ______.


Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye 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 ______.


There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C25C2.


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.


There are 10 professors and 20 lecturers out of whom a committee of 2 professors and 3 lecturer is to be formed. Find:

C1 C2
(a) In how many ways committee: can be formed (i) 10C2 × 19C3 
(b) In how many ways a particular: professor is included (ii) 10C2 × 19C2
(c) In how many ways a particular: lecturer is included (iii) 9C1 × 20C3
(d) In how many ways a particular: lecturer is excluded (iv) 10C2 × 20C3

The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` is ______.


A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.


There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.


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 ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×