The number of 6 digit telephone numbers having atleast one of their digits repeated is

Question

The number of 6 digit telephone numbers having atleast one of their digits repeated is (A) 106- 10 P5 (B) 106- 10 P6 (C) 106- 10 P8 (D) 106

Tardigrade Admin · Accepted Answer

The number of 6 digit telephone numbers. Using digits 0,1 ldots ldots .9 is 106. The number of 6 -digit telephone numbers. Which have none of their digits repeated is 10 P6. Required ways =106- 10 P6

Q. The number of $6$ digit telephone numbers having atleast one of their digits repeated is

$1 0^{6} -^{10} P_{5}$

$1 0^{6} -^{10} P_{6}$

$1 0^{6} -^{10} P_{8}$

$1 0^{6}$

None of these.

The number of $6$ digit telephone numbers.
Using digits $0, 1 \dots\dots .9$ is $1 0^{6}$ .
The number of $6$ -digit telephone numbers.
Which have none of their digits repeated is $^{10} P_{6}$ .
Required ways $= 1 0^{6} -^{10} P_{6}$

Q. The number of 6 digit telephone numbers having atleast one of their digits repeated is

106−10P5​

106−10P6​

106−10P8​

106