Answer:
Step-by-step explanation:
As there are total 52 cards in a deck and we have to draw a set of 5 cards, we can use the formula of combination to find the total number of possible ways of drawing 5 cards.
Number of ways to draw 5 cards = 
(a) Assuming the cards are drawn in order (would not affect the probability). The of getting Ace, 2, 3, 4 and 5 can be obtained by multiplying the probability of getting cards below 6 (20/52) with the probability of getting 5 different cards (4 choices for each card).
(b) For a straight we require our set to be in a sequence. The choices for lowest value card to produce a sequence are ace, 2, 3, 4, 5, 6, 7, 8, 9, or 10. Hence, the number of ways are 
.
For each card we can draw from any of the 4 sets. It can be described mathematically as: ![({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)*({}^{4}C_1)\;=\;[({}^{4}C_1)^5]](https://tex.z-dn.net/?f=%28%7B%7D%5E%7B4%7DC_1%29%2A%28%7B%7D%5E%7B4%7DC_1%29%2A%28%7B%7D%5E%7B4%7DC_1%29%2A%28%7B%7D%5E%7B4%7DC_1%29%2A%28%7B%7D%5E%7B4%7DC_1%29%5C%3B%3D%5C%3B%5B%28%7B%7D%5E%7B4%7DC_1%29%5E5%5D)
Therefore, the total outcomes for drawing straight are:
Thus, the probability of getting a straight hand is:
