2. Hexadecimal digits are formed using either a numeric decimal digit or a lette

Question

2. Hexadecimal digits are formed using either a numeric decimal digit or a letter from A to F. How many possible digits can be chosen? Did you use the sum rule or the product rule?

3. A combination lock requires three numbers from 1 to 25. How many combinations are possible? Did you use the sum rule or the product rule? (Note that although we use the term combination with locks, order matters.)

4. Use the permutation formula to calculate the number permutations of the set {a, b, c, d} taken two at a time. Also list these permutations.

Explanation / Answer

2. Let X be a set of Hexadecimal Integers = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Let X be a set of Hexadecimal Letters= {A, B, C, D, E, F}.

The rule of sum states that if Task A can be done in m ways & if Task B can be done in n ways.Then either tasks can be done m+n ways.Hence we add the total elements of X and Y i.e, 10 + 6 = 16.

3.Since each different selection can be from 1-25(repetition is allowed),

we can use the Multiplication Rule to solve:

(25)(25)(25) = 253 = 15625 So there are 15625 combinations. [ (25)(24)(23) if repetition is not allowed]

4. P(n,k) = n(n-1)(n-2)...(n-k+1)
Put n=4 and k=2 and get -

P(4,2) = 4 times 3 = 12.

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