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Re: How many two-digit numbers can be formed from the digits 1 t [#permalink]
18 Mar 2020, 08:27

Expert's post

GeminiHeat wrote:

How many two-digit numbers can be formed from the digits 1 through 9, if no digit appears twice in a number?

(A) 36 (B) 72 (C) 81 (D) 144 (E) 162

Take the task of creating 2-digit numbers and break it into stages.

Stage 1: Select a tens digit We can choose 1, 2, 3, 4, 5, 6, 7, 8 or 9 So, we can complete stage 1 in 9 ways

Stage 2: Select the units digit Since we can't choose the same digit we chose in stage 1, we can complete this stage in 8 ways.

By the Fundamental Counting Principle (FCP), we can complete the 2 stages (and thus create a 2-digit number) in (9)(8) ways (= 72 ways)

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. For more information about the FCP, watch these videos:

Fundamental Counting Principle Example:

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Re: How many two-digit numbers can be formed from the digits 1 t [#permalink]
01 Aug 2020, 04:10

we asked to form 2-digit number containing numbers from 1-9 without repetition. First digit will have any number from 1 to 9, can be formed in 9 way second digit can be formed in 8 ways. therefore, total ways to form that number = 9*8=72 answer is B

Re: How many two-digit numbers can be formed from the digits 1 t [#permalink]
03 Aug 2020, 03:59

1

This post received KUDOS

Experiment: Find all the possible two digit numbers that only use digits 1-9 and no digit repeats. Event1: choose a digit for your tens place Event2: choose a digit for your ones place

Number of possible outcomes for Event1: 9 Namely: 1,2,3,4,5,6,7,8,9

Number of possible of outcomes for Event2: 8 Namely: we can choose any number from 1 to 9 except the one chosen in Event1

By Fundamental Counting Principle: # of outcomes in the entire experiment is the product of the number of possible outcomes in both events. 9*8=72

But why can we use Fundamental Counting Principle? B/C no matter what number we choose in Event1 we'll always have 8 possible outcomes in Event2. That is, the NUMBER of possible outcomes of each event is independent of one another. If the number of possible outcomes between both events was not independent then we wouldn't be able to use Fundamental Counting Principle.