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 4! – 3!
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
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?
Which of the following are true:
(2 +3)! = 2! + 3!
Which of the following are true:
(2 × 3)! = 2! × 3!
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?
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:
Evaluate each of the following:
P(6, 4)
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
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 5 boys and 3 girls can be seated in a row so that each girl is between 2 boys ?
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
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 words from the letters of the word 'BHARAT' in which B and H will never come together, is
The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
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
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
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
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?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
How many ways can the product a2 b3 c4 be expressed without exponents?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
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 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
