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# How many two-digit numbers can be formed from the digits 1 t

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How many two-digit numbers can be formed from the digits 1 t [#permalink]  17 Mar 2020, 00:36
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Question Stats:

71% (00:24) correct 28% (00:07) wrong based on 21 sessions
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
[Reveal] Spoiler: OA
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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)

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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Manager
Joined: 02 Sep 2019
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Concentration: Finance
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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
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Re: How many two-digit numbers can be formed from the digits 1 t [#permalink]  03 Aug 2020, 03:59
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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.
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Re: How many two-digit numbers can be formed from the digits 1 t [#permalink]  04 Aug 2020, 13:09
An alternative method would be to use the process of elimination. There are 100 numbers between 1 and 100 inclusive.

1. Remove 100 and the nine single digit numbers. We are down to 90 numbers.

2. Next, remove the nine two-digit numbers which have the same tens and ones digit. We are down to 81 numbers.

3. Finally, remove the nine two digit numbers ending in zero. We are down to 72 numbers, and thus the answer is B.
Re: How many two-digit numbers can be formed from the digits 1 t   [#permalink] 04 Aug 2020, 13:09
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