Advertisements
Advertisements
Question
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?
Advertisements
Solution
Given that each number starts at 67, we need a five-digit number. So we have to fill only one’s place, 10’s place, and 100th place. From 0 to 9 there are 10 digits. In these digits, 6 and 7 should not be used as a repetition of digits is not allowed. Except for these two digits, we have 8 digits. Therefore one’s place can be filled by any of the 8 digits in 8 different ways. Now there are 7 digits are left.
Therefore 10’s place can be filled by any of the 7 digits in 7 different ways. Similarly, 100th place can be filled in 6 different ways. By multiplication principle, the number of telephone numbers constructed is 8 × 7 × 6 = 336.
APPEARS IN
RELATED QUESTIONS
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)` when n = 6, r = 2
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?
Three dice are rolled. Find the number of possible outcomes in which at least one die shows 5 ?
Write the number of arrangements of the letters of the word BANANA in which two N's come together.
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Choose the correct alternative:
The product of r consecutive positive integers is divisible b
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?
If 1P1 + 2. 2p2 + 3. 3p3 + ....... 15. 15P15 = qPr – s, 0 ≤ s ≤ 1, then q+sCr–s is equal to ______.
