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?
It is given that the 5-digit telephone numbers always start with 67.
Therefore, there will be as many phone numbers as there are ways of filling 3 vacant places
| 6 | 7 |
by the digits 0 – 9, keeping in mind that the digits cannot be repeated.
The units place can be filled by any of the digits from 0 – 9, except digits 6 and 7. Therefore, the units place can be filled in 8 different ways following which, the tens place can be filled in by any of the remaining 7 digits in 7 different ways, and the hundreds place can be filled in by any of the remaining 6 digits in 6 different ways.
Therefore, by multiplication principle, the required number of ways in which 5-digit telephone numbers can be constructed is 8 × 7 × 6 = 336
Popular Questions of Class 11 Mathematics
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- Q:-
If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.
- Q:-
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
- Q:- Find the sum of all natural numbers lying between 100 and 1000, which are multiples of 5.
- Q:-
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.
- Q:-
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
- Q:-
Find the sum of all numbers between 200 and 400 which are divisible by 7.
- Q:- Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER. - Q:-
Insert five numbers between 8 and 26 such that the resulting sequence is an A.P.
- Q:-
Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.
Recently Viewed Questions of Class 11 Mathematics
- Q:-
How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
- Q:-
How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?
- Q:-
How many 3-digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
- Q:-
The 4th term of a G.P. is square of its second term, and the first term is –3. Determine its 7th term.
- Q:- Write the first five terms of the sequences whose nth term is \begin{align} a_n = \frac {n}{n+1}\end{align}
- Q:-
One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
- Q:-
Find the sum of integers from 1 to 100 that are divisible by 2 or 5.
- Q:-
Name the octants in which the following points lie:
(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)
- Q:-
Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer. - Q:-
Find the derivative of x at x = 1.
2 Comment(s) on this Question
Thank u Very much sir
Thanks sir
- NCERT Chapter