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
Compute `(8!)/(6! xx 2!)`
Find n if n – 1P3 : nP4 = 1 : 9
Find r if `""^5P_r = ""^6P_(r-1)`
How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
(i) 4 letters are used at a time,
(ii) all letters are used at a time,
(iii) all letters are used but first letter is a vowel?
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
Find x in each of the following:
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many numbers of four digits can be formed with the digits 1, 2, 3, 4, 5 if the digits can be repeated in the same number?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 4 letters be posted in 5 letter boxes?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
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 words that can be formed out of the letters of the word 'COMMITTEE' ?
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 ?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of ways to arrange the letters of the word CHEESE are
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
If nP4 = 12(nP2), find n.
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if question number n has n + 1 choices?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
Find the distinct permutations of the letters of the word MISSISSIPPI?
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 of these 6-digit numbers are divisible by 4?
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
If all permutations of the letters of the word AGAIN are arranged in the order as in a dictionary. What is the 49th word?
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
