Question

The number of five-digit telephone numbers having at least one of their digits repeated is
A.90000
B.100000
C.30240
D.69760

Answer 1

To calculate numbers without repetition every new number multiplied is one less than the previous and in with repletion as there are total 10 digits; 10 is multiplied 5 times.

Complete step-by-step answer:
Firstly we need to find the numbers with repetition. This we can easily find out by multiplying 10 with it 5 times. We are doing this because there are 10 digits and the number is a five-digit one
Numbers with repetition=$10 \times 10 \times10 \times10 \times10$
=1, 00,000
Next, we need to find out the numbers without repetition. We can do this my starting from 10 and multiplied 5 numbers with each number one less than the previous
Numbers without repetition =$10 \times 9 \times 8 \times 7 \times 6$
=30240
When we subtract the two values we need the number with one of its digit repeated
Number with one digit is repeated=100000−30240
=69760
Hence, the number of 5 digit telephone numbers having least one of their digits repeated is 69760
Therefore, the correct option is (d).

Note: Students often go wrong by forgetting to subtract the value with no repetition. This is a very important step otherwise it is impossible to get an answer with only one digit repeated.