how many 10 digit numbers can be formed by using digits 3 and 5?
Answers
Answer:
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Step-by-step explanation:
1024 (2 to the power of 10):
1111111111
1111111112
1111111121
1111111122
1111111211
…
2222222222
Look at it like this:
How many 1-digit numbers? 2 (1 and 2)
How many 2-digit numbers? 4 (the number of 1-digit numbers times 2: 11, 12, 21, 22)
How many 3-digit numbers? 8 (the number of 2-digit numbers times 2: 111, 112, 121, 122, 211, 212, 221, 222
etc.
Each time, there’s double the number of numbers than before, hence [math]2^{10}[/math].
2.How many 10-digit numbers can be written by using the digits 1 and 2?
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1024 (2 to the power of 10):
1111111111
1111111112
1111111121
1111111122
1111111211
…
2222222222
Look at it like this:
How many 1-digit numbers? 2 (1 and 2)
How many 2-digit numbers? 4 (the number of 1-digit numbers times 2: 11, 12, 21, 22)
How many 3-digit numbers? 8 (the number of 2-digit numbers times 2: 111, 112, 121, 122, 211, 212, 221, 222
etc.
Each time, there’s double the number of numbers than before, hence [math]2^{10}[/math].
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Ans.: 1024
One can use a simple formula that comes from the logical field of probability and progressions to answer this question.
m^n
Where,
m=Number of unique instances
n=Number of instances required per combination of the unique instances.
So, here
m=2 (1 and 2)
n=10 (10 digits)
➡m^n=2^10
=1024