8. Find \( r \) if: \( { }^{5} P_{r}=2^{\circ} \mathrm{P}_{t-1} \) 9. What is the number of ways of choosing 4 cards from a pack of 52 playing cards? i) Four cards are of the same suit? ii) Cards are of the same colour?

If you draw a card from a deck and do not replace it, what type of events does this represent when drawing a second card?

Explain why choosing two socks from a drawer containing blue, red, and green socks is an example of dependent events.

23. What is the probability that a random arrangement of the letters of the word RESUME has an E on each end? A. 0.067 B. 0.076 C. 0.089 D. 0.095

The chance of winning a particular lottery game is 1 in 32000, How many tickets would I need to buy in order to improve the chance to 1 in 3200 ? If a machine produces 40 items in 5 minutes, how many liems would it produce in a day?

Find c.df \( f(x) \) and \( P\left(\frac{1}{3}<x<\frac{1}{3}\right) \) of the Eollowing \[ \begin{aligned} f(x)=12 x^{2}(1-x) & \text { For } 0<x<1 \\ =0 & \text { otherwise }\end{aligned} \]