Discrete mathematics for CS questions. Discrete mathematics for CS questions. 1.

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Discrete mathematics for CS questions.

Discrete mathematics for CS questions. 1. How many ternary strings of length 16 have exactly four 0s? 2. How many ternary strings of length 16 have exactly four 0s and exactly 3 1s? 3. How many hexadecimal strings of length n have at least 2 fs? 4. How many binary strings of length 23 start 010? 5. How many binary strings of length 25 are palindromes read the same left to right and right to left) that start with 00? 6. How many many words from the Roman alphabet of length 30 have three Bs, or 5 Ks, or 7 Zs? Prove the following identity for positive integers a, b, and c, with a

Explanation / Answer

3)

Generally 16n hexadecimal strings of length n.

Consider length n=2.

Then the resul of hexadecimal strings=162 =256

4) Consider,

string length is 23.

There are two choices, either 0 nor 1 for each element in the string. Hence, there are 223 possible strings.

So, there are 223 binary strings of length 23.

5)

The strings of length n are palindromes=2(n+1)/2 for odd and 2n/2 for even.

Consider strings of length n=25 is odd.

Then the result of binary=2(25+1)/2 =8192 .

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