Advertisements
Advertisements
प्रश्न
In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
Advertisements
उत्तर
If first two digits is 41, then the remaining 4 digits can be arranged in 8P4 ways
= `(8!)/((8 - 4)!)`
= `(8!)/(4!)`
= `(8 xx 7 xx 6 xx 5 xx 4!)/(4!)`
= 1680
Similarly, first two digits can be 42 or 46 or 62 or 64.
∴ Total number of telephone numbers have all digits distinct = 5 × 1680 = 8400
Hence, the required telephone numbers = 8400
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
Is 3! + 4! = 7!?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
In how many ways can 5 different balls be distributed among three boxes?
In how many ways can 7 letters be posted in 4 letter boxes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
P(6, 4)
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
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
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
If (n+2)! = 60[(n–1)!], find n
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
Find the number of arrangements that can be made out of the letters of the word “ASSASSINATION”.
Evaluate the following.
`(3! + 1!)/(2^2!)`
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The number of ways to arrange the letters of the word “CHEESE”:
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
A coin is tossed 8 times, how many different sequences containing six heads and two tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
In how many ways can 5 children be arranged in a line such that two particular children of them are always together
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place 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! |
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
