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How many 10-digit numbers can be formed using only the digit

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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How many 10-digit numbers can be formed using only the digit [#permalink] New post 30 Jul 2018, 10:49
Expert's post
00:00

Question Stats:

81% (00:38) correct 18% (00:28) wrong based on 11 sessions
How many 10-digit numbers can be formed using only the digits 2 and 5?

(A) \(2^{10}\)
(B) \((22)(5!)\)
(C) \((5!)(5!)\)
(D) \(\frac{10!}{2!}\)
(E) \(10!\)
[Reveal] Spoiler: OA

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Sandy
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4750
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1665 [0], given: 396

CAT Tests
Re: How many 10-digit numbers can be formed using only the digit [#permalink] New post 07 Aug 2018, 16:49
Expert's post
Explanation

This problem relies on the fundamental counting principle, which says that the total number of ways for something to happen is the product of the number of options for each individual choice.

For any digit of the 10-digit number there are exactly two options, a 2 or a 5. Thus, since there are two choices for each digit and it is a 10-digit number, there are \((2)(2)(2)(2)(2)(2)(2)(2)(2)(2) = 2^{10}\) total choices.
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Sandy
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Re: How many 10-digit numbers can be formed using only the digit   [#permalink] 07 Aug 2018, 16:49
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How many 10-digit numbers can be formed using only the digit

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