A “descending number” is a three-digit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a three-digit number chosen at random is a “descending number”?
(A) 3/25
(B) 2/9
(C) 2/15
(D) 1/9
(E) 1/10

Question

A “descending number” is a three-digit number, such that the units digit is less than the tens digits and the tens digit is less than the hundreds digit. What is the probability that a three-digit number chosen at random is a “descending number”?
(A)  3/25
(B)  2/9
(C)  2/15
(D)  1/9
(E)  1/10

kc_kennylau · Answer

How many descending numbers are there?

kc_kennylau · Answer

1. How many 3-digit-numbers are there that have different units, tens and hundreds digits? ("descending number" can't have repeated digits)
2. Divide that by 6 (123,132,213,231,312,321 6 combinations for the same group)

ranga · Answer

Arrange the numbers in descending order:
9    8    7    6    5    4    3    2    1    0

Remove any 7 digits out of this and you will always end up with a 3 digit number in descending order.  

In how many ways can we remove 7 numbers out of these 10 numbers?  10C7
10! / (7! * 3!) = 120.

There are a total of 900 3 digit numbers from 100 to 999.

So the probability of getting a descending 3 digit number is:  120 / 900 = 2/15

Answer: C) 2/15

kc_kennylau · Answer

@ranga lolz I thought he didn't know C so I didn't use it

anonymous · Answer

You are amazing....@ranga

anonymous · Answer

@ranga