Three-digit numbers are formed using the digits 0 , 2,4,6,8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

Question

Three-digit numbers are formed using the digits 0 , 2,4,6,8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits? (A) (1/16) (B) (16/25) (C) (1/645) (D) (1/25)

Tardigrade Admin · Accepted Answer

Since, a 3-digit number cannot start with digit 0 , the hundredth place can have any of the 4 digits. Now, the tens and units place can have all the 5-digits. Therefore, the total possible 3-digit numbers are

4 \times 5 \times 5

i.e.,

100

.
The total possible 3-digit numbers having all digits same

= 4

Hence,

P

(3-digit number with same digits)

= \frac{4}{100} = \frac{1}{25}

Q. Three-digit numbers are formed using the digits $0, 2, 4, 6, 8$ . A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

$\frac{1}{16}$

$\frac{16}{25}$

$\frac{1}{645}$

$\frac{1}{25}$

Q. Three-digit numbers are formed using the digits 0,2,4,6,8. A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

161​

2516​

6451​

251​

Q. Three-digit numbers are formed using the digits $0, 2, 4, 6, 8$ . A number is chosen at random out of these numbers. What is the probability that this number has the same digits?

$\frac{1}{16}$

$\frac{16}{25}$

$\frac{1}{645}$

$\frac{1}{25}$