Advertisements
Advertisements
Question
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
Options
90,000
10,000
30,240
69,760
Advertisements
Solution
The number of 5-digit telephone numbers having atleast one of their digits repeated is 69,760.
Explanation:
Total number of 5-digit telephone number if all the digits are repeated = (10)5 ......[∵ Digits are from 0 to 9]
If digits are not repeated, then 5-digit telephones, can be formed in 10P5 ways
∴ Required number of ways = (10)5 – 10P5
= `100000 - (10!)/((10 - 5)!)`
= `100000 - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5!)`
= 100000 – 30240
= 69760
APPEARS IN
RELATED QUESTIONS
Is 3! + 4! = 7!?
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit 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?
Find r if `""^5P_r = 2^6 P_(r-1)`
In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?
Find x in each of the following:
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
Find the number of ways in which one can post 5 letters in 7 letter boxes ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
Evaluate each of the following:
6P6
Evaluate each of the following:
P(6, 4)
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
Write the number of ways in which 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
How many numbers greater than 10 lacs be formed from 2, 3, 0, 3, 4, 2, 3 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
The number of different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, is
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many 6-digit telephone numbers can be constructed with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 if each numbers starts with 35 and no digit appear more than once?
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
The number of permutation of n different things taken r at a time, when the repetition is allowed is:
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if the vowels and consonants are alternative
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many distinct 6-digit numbers are there?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are even?
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
The total number of 9 digit numbers which have all different digits is ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
