Advertisements
Advertisements
प्रश्न
How many 5-digit telephone numbers can be constructed using the digits 0 to 9. If each number starts with 67 and no digit appears more than once?
Advertisements
उत्तर
It is given that 5-digit telephone numbers always begin with 67.
Therefore, there are as many ways to fill the 3-digit numbers as there are phone numbers 
with the digits 0–9, keeping in mind that digits cannot be repeated.
The units place can be filled with any of the digits 0–9, except digits 6 and 7, in 7 different ways, and the hundreds place can be filled with any of the remaining 6 digits in 6 different ways.
Therefore, by the multiplication principle, the required number of ways to form 5-digit telephone numbers is 8 × 7 × 6 = 336.
APPEARS IN
संबंधित प्रश्न
Is 3! + 4! = 7!?
Find r if `""^5P_r = 2^6 P_(r-1)`
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
Which of the following are true:
(2 × 3)! = 2! × 3!
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Evaluate each of the following:
6P6
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
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 number of arrangements of the letters of the word BANANA in which two N's come 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 6 men and 5 women can dine at a round table if no two women sit together ?
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
Number of all four digit numbers having different digits formed of the digits 1, 2, 3, 4 and 5 and divisible by 4 is
The product of r consecutive positive integers is divisible by
Find x if `1/(6!) + 1/(7!) = x/(8!)`
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`((3!)! xx 2!)/(5!)`
The possible outcomes when a coin is tossed five times:
The total number of 9 digit number which has all different digit is:
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 are there using the letters of the word INTERMEDIATE, if vowels are never together
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Choose the correct alternative:
If `""^(("n" + 5))"P"_(("n" + 1)) = ((11("n" - 1))/2)^(("n" + 3))"P"_"n"`, then the value of n are
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 ______.
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
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?
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
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! |
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
If m+nP2 = 90 and m–nP2 = 30, then (m, n) is given by ______.
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 ______.
