The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is:
(a)<math>16/25</math> (b)<math>(9/10)^3</math> (c)<math>27/75</math> (d)<math>18/25</math>
First digit can be chosen in $8$ ways from $1-9$ excluding $7$
Second digit can be chosen in $9$ ways from $0-9$ excluding $7$ and similarly the third digit in $9$ ways.
So, total no. of ways excluding $7 = 8*9*9$
Total no. of ways including $7 = 9 * 10 * 10$
So, ans = $(8*9*9)/(9*10*10) = 18/25$
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is:
(a)<math>16/25</math> (b)<math>(9/10)^3</math> (c)<math>27/75</math> (d)<math>18/25</math>
First digit can be chosen in $8$ ways from $1-9$ excluding $7$
Second digit can be chosen in $9$ ways from $0-9$ excluding $7$ and similarly the third digit in $9$ ways.
So, total no. of ways excluding $7 = 8*9*9$
Total no. of ways including $7 = 9 * 10 * 10$
So, ans = $(8*9*9)/(9*10*10) = 18/25$
GATECSE