# CMI2020-A: 6

21 views

There are $n$ songs segregated into $3$ playlists. Assume that each playlist has at least one song. For all $n$, the number of ways of choosing three songs consisting of one song from each playlist is:

1. $>\frac{n^3}{27}$
2. $\underline<\frac{n^3}{27}$
3. $\begin{pmatrix} n\\3 \end{pmatrix}$
4. $n^3$
in Others
edited

## Related questions

1
25 views
A password contains exactly $6$ characters. Each character is either a lowercase letter $\{a,b,\dots,z\}$ or a digit $\{ 0,1,\dots,9\}$. A valid password should contain at least one digit. What is the total number of valid passwords? Here is an incorrect answer ... Provide a justification for your answer. You do not need to simplify your expressions (for example, you can write $26^5, 5!, etc.$).
Which of the following languages over the alphabet $\{0,1\}$ are $not$ recognized by deterministic finite state automata $(DFA)$ with $three$ states? Words which do not have $11$ as a contiguous subword Binary representations of multiples of three Words that have $11$ as a suffix Words that do not contain $101$ as a contiguous subword
Consider the following regular expressions over alphabet$\{a,b\}$, where the notation $(a+b)^+$ means $(a+b)(a+b)^*$: $r_1=(a+b)^+a(a+b)^*$ $r_2=(a+b)^*b(a+b)^+$ Let $L_1$ and $L_2$ be the languages defined by $r_1$ and $r_2$, respectively. Which of the following regular expressions define $L_1\cap L_2$ ... $(a+b)^*a\;b(a+b)^*$ $(a+b)^*b(a+b)^*a(a+b)^*$ $(a+b)^*a(a+b)^*b(a+b)^*$