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How many 10-digit numbers can be formed using only the digit
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30 Jul 2018, 10:49
30 Jul 2018, 10:49
Expert Reply
00:00
Question Stats:
81% (00:33) correct
18% (01:03) wrong based on 66 sessions
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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) \(10!\)
(A) \(2^{10}\)
(B) \((22)(5!)\)
(C) \((5!)(5!)\)
(D) \(\frac{10!}{2!}\)
(E) \(10!\)
Re: How many 10-digit numbers can be formed using only the digit
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07 Aug 2018, 16:49
07 Aug 2018, 16:49
3
Expert Reply
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.
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.
Re: How many 10-digit numbers can be formed using only the digit
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02 Jun 2021, 19:04
02 Jun 2021, 19:04
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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