The password to an iPad is a 4-digit code. Each digit can be 0 to 9. How many po

Question

The password to an iPad is a 4-digit code. Each digit can be 0 to 9. How many possible passwords are there? How many possible passwords with four different digits are there? Human genetic material (DNA) is made up of sequences of molecules adensosine(A), guanine (G), cytosine (C), and thymine (T), which are called bases. A codon is a sequence of three bases. Replicates are allowed, so AAA, CCC, and so forth are codons. How many different codons are there? How many codons are there in what all three bases are different? How many codons are there that does not contain adencsine A?

Explanation / Answer

I am able to give you nswer for the first part of first question:

a)

Since you can repeat the digits the NUMBER of 4 digit combinations is relatively easy to calculate. Suppose that you are going to write one of these 4 digit combinations. You have 10 choices for the first digit. Once you have chosen the first digit you have 10 choices for the second digit. Thus you have 10x10 = 100 choices for the first two digits. For each choice of the first two digits you have 10 choices for the third digit. Thus you have 10x10x10 = 1000 choices for the first three digits. Finally you have 10 choices for the fourth digit and thus there are 10x10x10x10 = 10 000 possible 4 digit combinations from 0-9.

I am not going to list all 10 000 combinations but I will show you a way to do so in a "natural" order. The list will be in 1000 rows with 10 combinations in each row.

0000   0001   0002   0003   0004   ...   0008   0009
0010   0011   0012   0013   0014   ...   0018   0019
0020   0021   0022   0023   0024   ...   0028   0029
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.   .

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9980   9981   9982   9983   9984   ...   9988   9989
9990   9991   9992   9993   9994   ...   9998   9999

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