I2.1 Two cards are drawn at random from a pack and not replaced. Find the probability $\frac{1}{a}$ that both cards are hearts.

I2.2 If there are $b$ ways of choosing 15 people from ' $a$ ' people, find $b$.
I2.3 If $c$ signals can be made with $\frac{b}{2 a}$ flags of different colours by raising at least one of the flags, without considering the arrangement of colours, find $c$.

I2.4 There are $c$ balls in a bag, of which 3 are red. What is the probability of drawing a red ball?
$$
\begin{array}{l}
\mathrm{P}(\text { both hearts })=\frac{1}{a}=\frac{13}{52} \times \frac{12}{51}=\frac{1}{17} \\
a=17 \\
b=C_{15}^{17}=\frac{17 \times 16}{2}=136 \\
\frac{b}{2 a}=\frac{136}{2 \cdot 17}=4
\end{array}
$$

The following are different patterns: 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, where ' 0 ' in the $\mathrm{i}^{\text {ih }}$ position represents the $\mathrm{i}^{\text {th }}$ colour flag is put down and ' 1 ' represents the $\mathrm{i}^{\text {th }}$ colour flag is raised.
$$
\begin{array}{l}
c=15 \\
\mathrm{P}(\text { red ball })=\frac{3}{15}=\frac{1}{5}
\end{array}
$$