हिंदी

How Many Different Five-digit Number Licence Plates Can Be Made Iffirst Digit Cannot Be Zero and the Repetition of Digits is Not Allowed, - Mathematics

Advertisements
Advertisements

प्रश्न

How many different five-digit number licence plates can be made if

first digit cannot be zero and the repetition of digits is not allowed,

उत्तर

(i) Since the first digit cannot be zero, the number of ways of filling the first digit = 9
 Number of ways of filling the second digit = 9     (Since repetition is not allowed)
 Number of ways of filling the third digit = 8
 Number of ways of filling the fourth digit = 7
 Number of ways of filling the fifth digit = 6
 Total number of licence plates that can be made = 9\[\times\]9\[\times\]8\[\times\]7\[\times\]6 = 27216

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 16: Permutations - Exercise 16.2 [पृष्ठ १५]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 11
अध्याय 16 Permutations
Exercise 16.2 | Q 19.1 | पृष्ठ १५

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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.


A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?


Compute: 

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


Compute:

\[\frac{11! - 10!}{9!}\]

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?


There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?


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


Since the  number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`


How many 9-digit numbers of different digits can be formed?


Evaluate the following:

12C10


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


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


In how many ways can a football team of 11 players be selected from 16 players? How many of these will

 exclude 2 particular players?


How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;


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


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 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 a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?


Find the number of (ii) triangles


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


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?


A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected.


Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines


Find the number of ways in which : (a) a selection


If 15C3r = 15Cr + 3 , then r is equal to


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


There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is


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.


There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?


The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______ 


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 ______.


A convex polygon has 44 diagonals. Find the number of its sides.


In how many ways can a football team of 11 players be selected from 16 players? How many of them will exclude 2 particular players?


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


15C8 + 15C915C615C7 = ______.


The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.


There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×