Using digits 0-9 how many 3 digit no can be formed such tha

Question

Using digits 0-9 how many 3 digit no can be formed such that digits are in descending order?

No OA or answer choices.

Bunuel · Answer

We can select any 3 digits out of 10, and arrange them in descending order. Note that there will be only one descending ordering for each triplet. For, example if we select 0, 3, 7, then the number satisfying the requirement will be 730.

Therefore the answer is simply  C^3_{10}=120 .

Hope it's clear.

bhidu · Answer

Brilliant!! Elegant solution...

himanshujovi · Answer

Bunuel isn't this solution a bit too simplistic. For eg say the digits are 6,6 and 6 ( no where mentioned that duplicates not allowed) . In that case no combination will be possible as the numbers are not in descending sequence.Am I looking too much into the problem ?

Bunuel · Answer

Intended meaning of the question is that we are choosing 3 digits out of {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, no repetitions.

suhaschan · Answer

The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in four colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?

A) 24 B)32 C)48 D)60 E)192

Can somebody please provide a lucid explanation?

A) 24 B)32 C)48 D)60 E)192

Can somebody please provide a lucid explanation?

Bunuel · Answer

This question is discussed here: the-carson-family-will-purchase-three-used-cars-there-are-128876.html P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html

hamzakb · Answer

I don't know if the following is right. Could you see and evaluate?

3 digits means 3 spaces have to be filled : __ __ __

the first space can contain all digits from (0-9) except 0 and 1. Because, then the requirement of descending order won't be filled. (e.g if first digit is 1, then second digit will be 0 and no option remaining for 3rd digit)

8 * __ * __

the second space can contain all digits except 9,0

8*8*__

the third space can contain all digits except 9,8

8*8*8

= 512

Bunuel · Answer

Your answer does not match the correct one (120), so obviously this approach is not right.

The problem with it is that if the first digit is say 2, then the options for the second one is just 2 not 8. So, writing 8*8*8 is wrong.

Using digits 0-9 how many 3 digit no can be formed such tha

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