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Bunuel
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How many 10-digit numbers can be formed using only the digits 2 and 5? 16 May 2022, 07:45
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78% (00:55) correct 22% (01:27) wrong based on 184 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) 10!/2
(E) 10!
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anusurya
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How many 10-digit numbers can be formed using only the digits 2 and 5? 20 May 2022, 20:50
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As each place of 10 digit number can be filled in 2 ways so total ways will be 2*2*2..... 10 times, i.e 2^10 should be answer.
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How many 10-digit numbers can be formed using only the digits 2 and 5? 23 May 2022, 13:51
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It would be nice if somebody explain why it’s not
10!/2 (2! = 2)

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How many 10-digit numbers can be formed using only the digits 2 and 5? 23 May 2022, 14:29
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AlevtinaN
It would be nice if somebody explain why it’s not
10!/2 (2! = 2)

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If you ever struggle with figuring out which technique to use, try it on a much simpler version to see if you can figure out the method.

We need to pick from two options for each of ten slots.

Let's say we just want a one-digit number. Our only options are 2 and 5. Two options.
Let's say we wanted a two-digit number. Our options are 22, 25, 52, and 55. Four options.
Let's say we wanted a three-digit number. Our options are 222, 225, 252, 255, 522, 525, 552, and 555. Eight options.
Notice a pattern? We are multiplying by two each time. No factorials and no dividing by two, so the answer choice you've asked about won't fit our pattern.

Here's a bonus question for you:
When WOULD you want to include something like 10! in your calculations? Hint: you'll need more than two options at each decision point.
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How many 10-digit numbers can be formed using only the digits 2 and 5? 24 May 2022, 00:19
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ThatDudeKnows
AlevtinaN
It would be nice if somebody explain why it’s not
10!/2 (2! = 2)

Posted from my mobile device


If you ever struggle with figuring out which technique to use, try it on a much simpler version to see if you can figure out the method.

We need to pick from two options for each of ten slots.

Let's say we just want a one-digit number. Our only options are 2 and 5. Two options.
Let's say we wanted a two-digit number. Our options are 22, 25, 52, and 55. Four options.
Let's say we wanted a three-digit number. Our options are 222, 225, 252, 255, 522, 525, 552, and 555. Eight options.
Notice a pattern? We are multiplying by two each time. No factorials and no dividing by two, so the answer choice you've asked about won't fit our pattern.

Here's a bonus question for you:
When WOULD you want to include something like 10! in your calculations? Hint: you'll need more than two options at each decision point.
Show more

When I have , for example , 5 digits for create 5 number code and I can’t use one number twice ? And it will be 5, 5-1, 5-2 … pattern ?
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How many 10-digit numbers can be formed using only the digits 2 and 5? 09 Dec 2025, 09:06
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