Question

The number of five digit telephone numbers having at least one of their digits repeated is

Solution

Correct option is

69760

The number of five digit telephone numbers which can formed using the digits 0, 1, 2, … 9 is 105 (see example 19). The number of five digit telephone numbers which have none of their digits repeated is 10P5 = 30240. Thus, the required number of telephone numbers is 105 – 30240 = 69760.

SIMILAR QUESTIONS

Q1

The number of positive integral solutions of the equation  is

Q2

The exponent of 7 in 100C50 is

Q3

In the certain test there are n questions. In this test 2k students gave wrong answers to at least (n – k) questions, where k = 0, 1, 2, …, n. If the total number of wrong answer is 4095, then value of n is 

Q4

If n > 1 and n divides (n – 1)! + 1, then 

Q5

In a group of 8 girls, two girls are sisters. The number of ways in which the girls can sit so that two sisters are not sitting together is

Q6

The number of words that can be formed by using the letters of the word MATHEMATICS that start as well as end with T is

Q8

The number of subsets of the set A = {a1a2, … an} which contain even number of elements is

Q9

The number of ways in which we can post 5 letters in 10 letter boxes is

Q10

Let P be a prime number such that P  23. Let n = p! + 1. The number of primes in the list n + 1, n + 2, n + 3, … n + p – 1 is